S3: Phase planes (ver. 1)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -4 \, x + y + 15$

$y'= -x - 5 \, y + 9$

The isoclines cross at $$( 4 , 1 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 2)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x - 5 \, y - 25$

$y'= -2 \, x - 2 \, y + 8$

The isoclines cross at $$( 5 , -1 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 3)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x - 4 \, y + 19$

$y'= 4 \, x + 4 \, y - 12$

The isoclines cross at $$( -1 , 4 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a northeast arrow system, the top region has a northwest arrow system, the left region has a southwest arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 4)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -x + 3 \, y + 7$

$y'= -3 \, x - 5 \, y - 7$

The isoclines cross at $$( 1 , -2 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 5)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -2 \, x + 3 \, y - 10$

$y'= -2 \, x - 3 \, y - 10$

The isoclines cross at $$( -5 , 0 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 6)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x - 4 \, y + 4$

$y'= -2 \, x - 4 \, y + 24$

The isoclines cross at $$( 4 , 4 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 7)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 5 \, x - 4 \, y - 8$

$y'= -3 \, x - 4 \, y + 24$

The isoclines cross at $$( 4 , 3 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 8)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -5 \, x - 3 \, y + 35$

$y'= x - 5 \, y + 21$

The isoclines cross at $$( 4 , 5 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 9)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 2 \, x - 2 \, y - 6$

$y'= -3 \, x - 3 \, y - 3$

The isoclines cross at $$( 1 , -2 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 10)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -x - 5 \, y$

$y'= -x + 2 \, y + 7$

The isoclines cross at $$( 5 , -1 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 11)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -x + 2 \, y$

$y'= -x - 2 \, y$

The isoclines cross at $$( 0 , 0 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 12)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -5 \, x - 3 \, y + 3$

$y'= 5 \, x - 2 \, y + 2$

The isoclines cross at $$( 0 , 1 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 13)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -4 \, x - y - 8$

$y'= -2 \, x + y - 10$

The isoclines cross at $$( -3 , 4 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 14)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 2 \, x - 3 \, y - 2$

$y'= -3 \, x - 2 \, y - 23$

The isoclines cross at $$( -5 , -4 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 15)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -4 \, x - 4 \, y + 16$

$y'= -x + 4 \, y - 6$

The isoclines cross at $$( 2 , 2 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 16)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -4 \, x - y - 3$

$y'= -5 \, x + y - 6$

The isoclines cross at $$( -1 , 1 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 17)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x - 2 \, y + 2$

$y'= -5 \, x - 3 \, y - 8$

The isoclines cross at $$( -1 , -1 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 18)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x + 4 \, y - 11$

$y'= 2 \, x - 5 \, y - 15$

The isoclines cross at $$( 5 , -1 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 19)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 2 \, x + 4 \, y - 18$

$y'= 3 \, x - 2 \, y + 13$

The isoclines cross at $$( -1 , 5 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 20)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x - 5 \, y + 14$

$y'= -x - 2 \, y + 3$

The isoclines cross at $$( -1 , 2 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 21)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -2 \, x + 4 \, y + 14$

$y'= -4 \, x - 5 \, y - 37$

The isoclines cross at $$( -3 , -5 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 22)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -x - 5 \, y - 3$

$y'= 5 \, x - 3 \, y + 15$

The isoclines cross at $$( -3 , 0 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 23)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -2 \, x - 5 \, y - 28$

$y'= -x + 3 \, y + 8$

The isoclines cross at $$( -4 , -4 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 24)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -2 \, x + 2 \, y - 10$

$y'= -3 \, x - 5 \, y + 17$

The isoclines cross at $$( -1 , 4 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 25)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 5 \, x + 2 \, y - 6$

$y'= 4 \, x - 2 \, y + 6$

The isoclines cross at $$( 0 , 3 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 26)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 5 \, x - 5 \, y - 5$

$y'= -4 \, x - 3 \, y + 25$

The isoclines cross at $$( 4 , 3 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 27)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 2 \, x - y + 11$

$y'= 4 \, x + y + 13$

The isoclines cross at $$( -4 , 3 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a northeast arrow system, the top region has a northwest arrow system, the left region has a southwest arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 28)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -4 \, x - 4 \, y + 16$

$y'= 2 \, x - 2 \, y + 12$

The isoclines cross at $$( -1 , 5 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 29)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x - 2 \, y - 7$

$y'= -x - 3 \, y + 6$

The isoclines cross at $$( 3 , 1 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 30)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -4 \, x - 4 \, y + 4$

$y'= -x + 4 \, y - 14$

The isoclines cross at $$( -2 , 3 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 31)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x + 3 \, y + 9$

$y'= x - 5 \, y + 15$

The isoclines cross at $$( -5 , 2 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 32)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -5 \, x - 4 \, y + 4$

$y'= 5 \, x - 2 \, y + 2$

The isoclines cross at $$( 0 , 1 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 33)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x - y + 19$

$y'= -4 \, x - 4 \, y - 24$

The isoclines cross at $$( -5 , -1 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 34)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -2 \, x - 5 \, y + 22$

$y'= 5 \, x - 3 \, y + 7$

The isoclines cross at $$( 1 , 4 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 35)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 5 \, x - 4 \, y + 31$

$y'= -5 \, x - 4 \, y + 1$

The isoclines cross at $$( -3 , 4 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 36)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -x - 3 \, y + 1$

$y'= 2 \, x - 2 \, y - 10$

The isoclines cross at $$( 4 , -1 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 37)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -3 \, x - y + 11$

$y'= 2 \, x - 2 \, y - 2$

The isoclines cross at $$( 3 , 2 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 38)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -5 \, x + y - 12$

$y'= -4 \, x - y - 15$

The isoclines cross at $$( -3 , -3 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 39)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 2 \, x + 5 \, y + 9$

$y'= 2 \, x - y - 9$

The isoclines cross at $$( 3 , -3 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 40)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -x - 3 \, y - 7$

$y'= -4 \, x + y - 2$

The isoclines cross at $$( -1 , -2 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 41)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 2 \, x - 3 \, y + 19$

$y'= -5 \, x - 4 \, y + 10$

The isoclines cross at $$( -2 , 5 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 42)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 2 \, x + y - 2$

$y'= 4 \, x - 2 \, y + 12$

The isoclines cross at $$( -1 , 4 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 43)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 5 \, x - 5 \, y + 25$

$y'= -4 \, x - 3 \, y - 6$

The isoclines cross at $$( -3 , 2 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 44)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -2 \, x + 4 \, y + 10$

$y'= -x - 3 \, y - 20$

The isoclines cross at $$( -5 , -5 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 45)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -4 \, x - y + 17$

$y'= 2 \, x - 2 \, y - 6$

The isoclines cross at $$( 4 , 1 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 46)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= x - y + 5$

$y'= -2 \, x - 5 \, y + 11$

The isoclines cross at $$( -2 , 3 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 47)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 2 \, x - y - 10$

$y'= -2 \, x - y + 6$

The isoclines cross at $$( 4 , -2 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 48)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x + y + 16$

$y'= 5 \, x - 4 \, y + 20$

The isoclines cross at $$( -4 , 0 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 49)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -3 \, x - y - 3$

$y'= -5 \, x + 4 \, y + 12$

The isoclines cross at $$( 0 , -3 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 50)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x - 3 \, y - 19$

$y'= -2 \, x - 2 \, y - 8$

The isoclines cross at $$( 1 , -5 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 51)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x - 4 \, y + 1$

$y'= 5 \, x + y + 17$

The isoclines cross at $$( -3 , -2 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a northeast arrow system, the top region has a northwest arrow system, the left region has a southwest arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 52)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x + 3 \, y - 6$

$y'= 5 \, x - 3 \, y + 22$

The isoclines cross at $$( -2 , 4 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 53)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= x - 4 \, y + 1$

$y'= -x - 4 \, y + 7$

The isoclines cross at $$( 3 , 1 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 54)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x - 5 \, y + 2$

$y'= -x - 3 \, y + 8$

The isoclines cross at $$( 2 , 2 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 55)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -2 \, x - 4 \, y + 26$

$y'= -3 \, x + 5 \, y - 5$

The isoclines cross at $$( 5 , 4 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 56)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x + y - 1$

$y'= 3 \, x - 2 \, y - 9$

The isoclines cross at $$( 1 , -3 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 57)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x - 4 \, y - 20$

$y'= -4 \, x - 3 \, y - 1$

The isoclines cross at $$( 2 , -3 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 58)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -x - 2 \, y$

$y'= -x + y + 3$

The isoclines cross at $$( 2 , -1 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 59)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 2 \, x - 5 \, y - 19$

$y'= 2 \, x + y + 11$

The isoclines cross at $$( -3 , -5 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a northeast arrow system, the top region has a northwest arrow system, the left region has a southwest arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 60)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -5 \, x + 3 \, y - 9$

$y'= -2 \, x - 3 \, y - 12$

The isoclines cross at $$( -3 , -2 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 61)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -5 \, x - 4 \, y$

$y'= 3 \, x - 2 \, y + 22$

The isoclines cross at $$( -4 , 5 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 62)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 2 \, x - 2 \, y + 8$

$y'= -3 \, x - 2 \, y - 17$

The isoclines cross at $$( -5 , -1 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 63)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -2 \, x + y + 12$

$y'= -3 \, x - 2 \, y + 4$

The isoclines cross at $$( 4 , -4 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 64)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -4 \, x + y + 18$

$y'= -4 \, x - 3 \, y + 26$

The isoclines cross at $$( 5 , 2 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 65)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 5 \, x + 4 \, y - 7$

$y'= 2 \, x - 5 \, y - 16$

The isoclines cross at $$( 3 , -2 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 66)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= x - y - 3$

$y'= -3 \, x - 3 \, y - 15$

The isoclines cross at $$( -1 , -4 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 67)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -x - 4 \, y + 25$

$y'= x - 5 \, y + 20$

The isoclines cross at $$( 5 , 5 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 68)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x - 2 \, y + 20$

$y'= -4 \, x - 4 \, y$

The isoclines cross at $$( -4 , 4 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 69)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= x - 3 \, y + 4$

$y'= -x - 3 \, y + 2$

The isoclines cross at $$( -1 , 1 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 70)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x - y - 18$

$y'= -5 \, x - y + 18$

The isoclines cross at $$( 4 , -2 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 71)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= x - 2 \, y - 5$

$y'= -x - 4 \, y - 1$

The isoclines cross at $$( 3 , -1 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 72)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x + 2 \, y - 17$

$y'= 2 \, x - 3 \, y + 6$

The isoclines cross at $$( 3 , 4 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 73)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x - 3 \, y - 8$

$y'= -3 \, x - 2 \, y + 6$

The isoclines cross at $$( 2 , 0 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 74)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= x - 5 \, y + 13$

$y'= 3 \, x + 5 \, y - 1$

The isoclines cross at $$( -3 , 2 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a northeast arrow system, the top region has a northwest arrow system, the left region has a southwest arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 75)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -3 \, x - 3 \, y - 9$

$y'= 2 \, x - 5 \, y - 1$

The isoclines cross at $$( -2 , -1 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 76)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -5 \, x - 5 \, y + 30$

$y'= 3 \, x - 3 \, y - 12$

The isoclines cross at $$( 5 , 1 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 77)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x - 4 \, y - 4$

$y'= x + 2 \, y - 13$

The isoclines cross at $$( 5 , 4 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a northeast arrow system, the top region has a northwest arrow system, the left region has a southwest arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 78)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= x - 2 \, y + 13$

$y'= -2 \, x - 5 \, y + 19$

The isoclines cross at $$( -3 , 5 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 79)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -2 \, x - 4 \, y - 12$

$y'= -x + 2 \, y + 2$

The isoclines cross at $$( -2 , -2 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 80)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 5 \, x - 5 \, y + 5$

$y'= -3 \, x - 3 \, y + 21$

The isoclines cross at $$( 3 , 4 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 81)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 2 \, x - y - 12$

$y'= x + 2 \, y + 4$

The isoclines cross at $$( 4 , -4 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a northeast arrow system, the top region has a northwest arrow system, the left region has a southwest arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 82)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 5 \, x - y - 18$

$y'= -2 \, x - 4 \, y - 6$

The isoclines cross at $$( 3 , -3 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 83)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -3 \, x - 2 \, y - 22$

$y'= -x + y + 1$

The isoclines cross at $$( -4 , -5 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 84)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x + 2 \, y - 6$

$y'= x - y - 2$

The isoclines cross at $$( 2 , 0 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 85)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 5 \, x + 4 \, y + 5$

$y'= x - 3 \, y + 1$

The isoclines cross at $$( -1 , 0 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 86)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x - 4 \, y - 8$

$y'= -4 \, x - 4 \, y - 32$

The isoclines cross at $$( -3 , -5 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 87)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -x - 3 \, y + 14$

$y'= 4 \, x - 5 \, y + 29$

The isoclines cross at $$( -1 , 5 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 88)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -5 \, x - 4 \, y + 3$

$y'= 5 \, x - 4 \, y - 27$

The isoclines cross at $$( 3 , -3 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 89)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x - y - 15$

$y'= -4 \, x - 3 \, y + 7$

The isoclines cross at $$( 4 , -3 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 90)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -2 \, x + 3 \, y - 17$

$y'= -5 \, x - 2 \, y + 5$

The isoclines cross at $$( -1 , 5 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 91)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x - 5 \, y - 31$

$y'= -4 \, x - 5 \, y - 17$

The isoclines cross at $$( 2 , -5 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 92)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 4 \, x - y + 14$

$y'= -x - 5 \, y + 7$

The isoclines cross at $$( -3 , 2 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 93)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -5 \, x - y - 20$

$y'= 2 \, x - y + 8$

The isoclines cross at $$( -4 , 0 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 94)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 3 \, x + 4 \, y + 3$

$y'= 5 \, x - 2 \, y - 21$

The isoclines cross at $$( 3 , -3 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northeast arrow system, the top region has a southeast arrow system, the left region has a southwest arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 95)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= x - 3 \, y + 15$

$y'= 3 \, x + 5 \, y - 11$

The isoclines cross at $$( -3 , 4 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a northeast arrow system, the top region has a northwest arrow system, the left region has a southwest arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 96)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -4 \, x - y + 10$

$y'= -4 \, x + 4 \, y$

The isoclines cross at $$( 2 , 2 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a southwest arrow system, the top region has a northwest arrow system, the left region has a northeast arrow system, and the bottom region has a southeast arrow system.

S3: Phase planes (ver. 97)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -4 \, x - y - 16$

$y'= 4 \, x - 3 \, y + 16$

The isoclines cross at $$( -4 , 0 )$$, with $$x'=0$$ having a negative slope and $$y'=0$$ having a positive slope.

The right region has a northwest arrow system, the top region has a southwest arrow system, the left region has a southeast arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 98)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= x - 3 \, y - 12$

$y'= -3 \, x - 4 \, y - 29$

The isoclines cross at $$( -3 , -5 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southeast arrow system, the top region has a southwest arrow system, the left region has a northwest arrow system, and the bottom region has a northeast arrow system.

S3: Phase planes (ver. 99)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= -3 \, x + 5 \, y - 10$

$y'= -5 \, x - 5 \, y - 30$

The isoclines cross at $$( -5 , -1 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.

The right region has a southwest arrow system, the top region has a southeast arrow system, the left region has a northeast arrow system, and the bottom region has a northwest arrow system.

S3: Phase planes (ver. 100)

Draw a phase plane for the following system of ODEs. Include the isoclines $$x'=0,y'=0$$ and mark each of the resulting regions with an arrow system describing the directions of trajectories in that region.

$x'= 2 \, x - 2 \, y + 6$

$y'= -x - y - 1$

The isoclines cross at $$( -2 , 1 )$$, with $$x'=0$$ having a positive slope and $$y'=0$$ having a negative slope.