## F2b: Separation of variables (ver. 1)

Find the solution to the given IVP.

$y'=( 6 \, t )y\hspace{1em} y(0)= -e^{\left(-5\right)}$

$y= -e^{\left(3 \, t^{2} - 5\right)}$

## F2b: Separation of variables (ver. 2)

Find the solution to the given IVP.

$y'=( -6 \, t - 3 )y\hspace{1em} y(0)= -3 \, e^{\left(-1\right)}$

$y= -3 \, e^{\left(-3 \, t^{2} - 3 \, t - 1\right)}$

## F2b: Separation of variables (ver. 3)

Find the solution to the given IVP.

$y'=( -3 \, \cos\left(t\right) )y\hspace{1em} y(0)= 4$

$y= 4 \, e^{\left(-3 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 4)

Find the solution to the given IVP.

$y'=( -4 \, t - 2 )y\hspace{1em} y(0)= 2 \, e$

$y= 2 \, e^{\left(-2 \, t^{2} - 2 \, t + 1\right)}$

## F2b: Separation of variables (ver. 5)

Find the solution to the given IVP.

$y'=( 2 \, t - 2 )y\hspace{1em} y(0)= 4 \, e^{\left(-2\right)}$

$y= 4 \, e^{\left(t^{2} - 2 \, t - 2\right)}$

## F2b: Separation of variables (ver. 6)

Find the solution to the given IVP.

$y'=( 6 \, t - 1 )y\hspace{1em} y(0)= -3 \, e^{\left(-2\right)}$

$y= -3 \, e^{\left(3 \, t^{2} - t - 2\right)}$

## F2b: Separation of variables (ver. 7)

Find the solution to the given IVP.

$y'=( 3 \, \cos\left(t\right) )y\hspace{1em} y(0)= -1$

$y= -e^{\left(3 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 8)

Find the solution to the given IVP.

$y'=( 6 \, t + 1 )y\hspace{1em} y(0)= 3 \, e^{\left(-4\right)}$

$y= 3 \, e^{\left(3 \, t^{2} + t - 4\right)}$

## F2b: Separation of variables (ver. 9)

Find the solution to the given IVP.

$y'=( 2 \, \cos\left(t\right) )y\hspace{1em} y(0)= 3$

$y= 3 \, e^{\left(2 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 10)

Find the solution to the given IVP.

$y'=( -\cos\left(t\right) )y\hspace{1em} y(0)= -2$

$y= -2 \, e^{\left(-\sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 11)

Find the solution to the given IVP.

$y'=( \sin\left(t\right) )y\hspace{1em} y(0)= e^{\left(-1\right)}$

$y= e^{\left(-\cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 12)

Find the solution to the given IVP.

$y'=( \cos\left(t\right) )y\hspace{1em} y(0)= 4$

$y= 4 \, e^{\sin\left(t\right)}$

## F2b: Separation of variables (ver. 13)

Find the solution to the given IVP.

$y'=( \sin\left(t\right) )y\hspace{1em} y(0)= -3 \, e^{\left(-1\right)}$

$y= -3 \, e^{\left(-\cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 14)

Find the solution to the given IVP.

$y'=( \cos\left(t\right) )y\hspace{1em} y(0)= 1$

$y= e^{\sin\left(t\right)}$

## F2b: Separation of variables (ver. 15)

Find the solution to the given IVP.

$y'=( 2 \, \sin\left(t\right) )y\hspace{1em} y(0)= -2 \, e^{\left(-2\right)}$

$y= -2 \, e^{\left(-2 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 16)

Find the solution to the given IVP.

$y'=( -\sin\left(t\right) )y\hspace{1em} y(0)= -2 \, e$

$y= -2 \, e^{\cos\left(t\right)}$

## F2b: Separation of variables (ver. 17)

Find the solution to the given IVP.

$y'=( -4 \, t )y\hspace{1em} y(0)= e^{4}$

$y= e^{\left(-2 \, t^{2} + 4\right)}$

## F2b: Separation of variables (ver. 18)

Find the solution to the given IVP.

$y'=( -6 \, t + 1 )y\hspace{1em} y(0)= -4 \, e^{\left(-2\right)}$

$y= -4 \, e^{\left(-3 \, t^{2} + t - 2\right)}$

## F2b: Separation of variables (ver. 19)

Find the solution to the given IVP.

$y'=( \sin\left(t\right) )y\hspace{1em} y(0)= 2 \, e^{\left(-1\right)}$

$y= 2 \, e^{\left(-\cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 20)

Find the solution to the given IVP.

$y'=( 3 \, \sin\left(t\right) )y\hspace{1em} y(0)= 4 \, e^{\left(-3\right)}$

$y= 4 \, e^{\left(-3 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 21)

Find the solution to the given IVP.

$y'=( -2 \, t - 2 )y\hspace{1em} y(0)= -2 \, e$

$y= -2 \, e^{\left(-t^{2} - 2 \, t + 1\right)}$

## F2b: Separation of variables (ver. 22)

Find the solution to the given IVP.

$y'=( -3 \, \sin\left(t\right) )y\hspace{1em} y(0)= -4 \, e^{3}$

$y= -4 \, e^{\left(3 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 23)

Find the solution to the given IVP.

$y'=( 3 \, \sin\left(t\right) )y\hspace{1em} y(0)= -4 \, e^{\left(-3\right)}$

$y= -4 \, e^{\left(-3 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 24)

Find the solution to the given IVP.

$y'=( 4 \, t - 1 )y\hspace{1em} y(0)= 4 \, e$

$y= 4 \, e^{\left(2 \, t^{2} - t + 1\right)}$

## F2b: Separation of variables (ver. 25)

Find the solution to the given IVP.

$y'=( 4 \, t + 3 )y\hspace{1em} y(0)= -2 \, e^{3}$

$y= -2 \, e^{\left(2 \, t^{2} + 3 \, t + 3\right)}$

## F2b: Separation of variables (ver. 26)

Find the solution to the given IVP.

$y'=( -2 \, \sin\left(t\right) )y\hspace{1em} y(0)= -2 \, e^{2}$

$y= -2 \, e^{\left(2 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 27)

Find the solution to the given IVP.

$y'=( -\cos\left(t\right) )y\hspace{1em} y(0)= -2$

$y= -2 \, e^{\left(-\sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 28)

Find the solution to the given IVP.

$y'=( -\sin\left(t\right) )y\hspace{1em} y(0)= e$

$y= e^{\cos\left(t\right)}$

## F2b: Separation of variables (ver. 29)

Find the solution to the given IVP.

$y'=( 6 \, t - 1 )y\hspace{1em} y(0)= 4 \, e^{\left(-5\right)}$

$y= 4 \, e^{\left(3 \, t^{2} - t - 5\right)}$

## F2b: Separation of variables (ver. 30)

Find the solution to the given IVP.

$y'=( 3 \, \sin\left(t\right) )y\hspace{1em} y(0)= -e^{\left(-3\right)}$

$y= -e^{\left(-3 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 31)

Find the solution to the given IVP.

$y'=( 3 \, \sin\left(t\right) )y\hspace{1em} y(0)= e^{\left(-3\right)}$

$y= e^{\left(-3 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 32)

Find the solution to the given IVP.

$y'=( 4 \, t + 2 )y\hspace{1em} y(0)= 3 \, e^{3}$

$y= 3 \, e^{\left(2 \, t^{2} + 2 \, t + 3\right)}$

## F2b: Separation of variables (ver. 33)

Find the solution to the given IVP.

$y'=( 2 \, \cos\left(t\right) )y\hspace{1em} y(0)= -1$

$y= -e^{\left(2 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 34)

Find the solution to the given IVP.

$y'=( -3 \, \sin\left(t\right) )y\hspace{1em} y(0)= -2 \, e^{3}$

$y= -2 \, e^{\left(3 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 35)

Find the solution to the given IVP.

$y'=( -3 \, \sin\left(t\right) )y\hspace{1em} y(0)= -4 \, e^{3}$

$y= -4 \, e^{\left(3 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 36)

Find the solution to the given IVP.

$y'=( -6 \, t )y\hspace{1em} y(0)= 3 \, e^{\left(-3\right)}$

$y= 3 \, e^{\left(-3 \, t^{2} - 3\right)}$

## F2b: Separation of variables (ver. 37)

Find the solution to the given IVP.

$y'=( 6 \, t + 3 )y\hspace{1em} y(0)= 3 \, e^{\left(-2\right)}$

$y= 3 \, e^{\left(3 \, t^{2} + 3 \, t - 2\right)}$

## F2b: Separation of variables (ver. 38)

Find the solution to the given IVP.

$y'=( -2 \, t - 3 )y\hspace{1em} y(0)= -3 \, e^{3}$

$y= -3 \, e^{\left(-t^{2} - 3 \, t + 3\right)}$

## F2b: Separation of variables (ver. 39)

Find the solution to the given IVP.

$y'=( -6 \, t + 1 )y\hspace{1em} y(0)= 2 \, e^{\left(-1\right)}$

$y= 2 \, e^{\left(-3 \, t^{2} + t - 1\right)}$

## F2b: Separation of variables (ver. 40)

Find the solution to the given IVP.

$y'=( -\cos\left(t\right) )y\hspace{1em} y(0)= 3$

$y= 3 \, e^{\left(-\sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 41)

Find the solution to the given IVP.

$y'=( -2 \, \sin\left(t\right) )y\hspace{1em} y(0)= -3 \, e^{2}$

$y= -3 \, e^{\left(2 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 42)

Find the solution to the given IVP.

$y'=( 2 \, \sin\left(t\right) )y\hspace{1em} y(0)= 4 \, e^{\left(-2\right)}$

$y= 4 \, e^{\left(-2 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 43)

Find the solution to the given IVP.

$y'=( 2 \, t )y\hspace{1em} y(0)= -e^{2}$

$y= -e^{\left(t^{2} + 2\right)}$

## F2b: Separation of variables (ver. 44)

Find the solution to the given IVP.

$y'=( -2 \, t - 3 )y\hspace{1em} y(0)= 3 \, e^{\left(-5\right)}$

$y= 3 \, e^{\left(-t^{2} - 3 \, t - 5\right)}$

## F2b: Separation of variables (ver. 45)

Find the solution to the given IVP.

$y'=( \sin\left(t\right) )y\hspace{1em} y(0)= -2 \, e^{\left(-1\right)}$

$y= -2 \, e^{\left(-\cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 46)

Find the solution to the given IVP.

$y'=( 3 \, \sin\left(t\right) )y\hspace{1em} y(0)= 4 \, e^{\left(-3\right)}$

$y= 4 \, e^{\left(-3 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 47)

Find the solution to the given IVP.

$y'=( \sin\left(t\right) )y\hspace{1em} y(0)= 2 \, e^{\left(-1\right)}$

$y= 2 \, e^{\left(-\cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 48)

Find the solution to the given IVP.

$y'=( 2 \, t + 1 )y\hspace{1em} y(0)= 2 \, e^{4}$

$y= 2 \, e^{\left(t^{2} + t + 4\right)}$

## F2b: Separation of variables (ver. 49)

Find the solution to the given IVP.

$y'=( -3 \, \cos\left(t\right) )y\hspace{1em} y(0)= -3$

$y= -3 \, e^{\left(-3 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 50)

Find the solution to the given IVP.

$y'=( 2 \, \cos\left(t\right) )y\hspace{1em} y(0)= 2$

$y= 2 \, e^{\left(2 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 51)

Find the solution to the given IVP.

$y'=( -3 \, \sin\left(t\right) )y\hspace{1em} y(0)= 2 \, e^{3}$

$y= 2 \, e^{\left(3 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 52)

Find the solution to the given IVP.

$y'=( 4 \, t )y\hspace{1em} y(0)= 2 \, e^{5}$

$y= 2 \, e^{\left(2 \, t^{2} + 5\right)}$

## F2b: Separation of variables (ver. 53)

Find the solution to the given IVP.

$y'=( 2 \, \sin\left(t\right) )y\hspace{1em} y(0)= 2 \, e^{\left(-2\right)}$

$y= 2 \, e^{\left(-2 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 54)

Find the solution to the given IVP.

$y'=( 3 \, \sin\left(t\right) )y\hspace{1em} y(0)= -4 \, e^{\left(-3\right)}$

$y= -4 \, e^{\left(-3 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 55)

Find the solution to the given IVP.

$y'=( -3 \, \cos\left(t\right) )y\hspace{1em} y(0)= 3$

$y= 3 \, e^{\left(-3 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 56)

Find the solution to the given IVP.

$y'=( -4 \, t + 2 )y\hspace{1em} y(0)= -3 \, e$

$y= -3 \, e^{\left(-2 \, t^{2} + 2 \, t + 1\right)}$

## F2b: Separation of variables (ver. 57)

Find the solution to the given IVP.

$y'=( 2 \, \cos\left(t\right) )y\hspace{1em} y(0)= -4$

$y= -4 \, e^{\left(2 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 58)

Find the solution to the given IVP.

$y'=( -\cos\left(t\right) )y\hspace{1em} y(0)= -2$

$y= -2 \, e^{\left(-\sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 59)

Find the solution to the given IVP.

$y'=( -\cos\left(t\right) )y\hspace{1em} y(0)= -4$

$y= -4 \, e^{\left(-\sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 60)

Find the solution to the given IVP.

$y'=( -2 \, t - 3 )y\hspace{1em} y(0)= 2 \, e^{\left(-2\right)}$

$y= 2 \, e^{\left(-t^{2} - 3 \, t - 2\right)}$

## F2b: Separation of variables (ver. 61)

Find the solution to the given IVP.

$y'=( -3 \, \sin\left(t\right) )y\hspace{1em} y(0)= -3 \, e^{3}$

$y= -3 \, e^{\left(3 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 62)

Find the solution to the given IVP.

$y'=( -2 \, t - 2 )y\hspace{1em} y(0)= -e$

$y= -e^{\left(-t^{2} - 2 \, t + 1\right)}$

## F2b: Separation of variables (ver. 63)

Find the solution to the given IVP.

$y'=( \sin\left(t\right) )y\hspace{1em} y(0)= 4 \, e^{\left(-1\right)}$

$y= 4 \, e^{\left(-\cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 64)

Find the solution to the given IVP.

$y'=( 6 \, t - 3 )y\hspace{1em} y(0)= 3 \, e^{3}$

$y= 3 \, e^{\left(3 \, t^{2} - 3 \, t + 3\right)}$

## F2b: Separation of variables (ver. 65)

Find the solution to the given IVP.

$y'=( -6 \, t )y\hspace{1em} y(0)= e^{\left(-2\right)}$

$y= e^{\left(-3 \, t^{2} - 2\right)}$

## F2b: Separation of variables (ver. 66)

Find the solution to the given IVP.

$y'=( 2 \, \cos\left(t\right) )y\hspace{1em} y(0)= -3$

$y= -3 \, e^{\left(2 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 67)

Find the solution to the given IVP.

$y'=( 6 \, t + 3 )y\hspace{1em} y(0)= 2 \, e^{\left(-4\right)}$

$y= 2 \, e^{\left(3 \, t^{2} + 3 \, t - 4\right)}$

## F2b: Separation of variables (ver. 68)

Find the solution to the given IVP.

$y'=( -\sin\left(t\right) )y\hspace{1em} y(0)= -2 \, e$

$y= -2 \, e^{\cos\left(t\right)}$

## F2b: Separation of variables (ver. 69)

Find the solution to the given IVP.

$y'=( 2 \, \sin\left(t\right) )y\hspace{1em} y(0)= e^{\left(-2\right)}$

$y= e^{\left(-2 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 70)

Find the solution to the given IVP.

$y'=( -6 \, t - 3 )y\hspace{1em} y(0)= -2 \, e^{4}$

$y= -2 \, e^{\left(-3 \, t^{2} - 3 \, t + 4\right)}$

## F2b: Separation of variables (ver. 71)

Find the solution to the given IVP.

$y'=( 2 \, \cos\left(t\right) )y\hspace{1em} y(0)= 1$

$y= e^{\left(2 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 72)

Find the solution to the given IVP.

$y'=( 2 \, \sin\left(t\right) )y\hspace{1em} y(0)= 4 \, e^{\left(-2\right)}$

$y= 4 \, e^{\left(-2 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 73)

Find the solution to the given IVP.

$y'=( 6 \, t )y\hspace{1em} y(0)= 1$

$y= e^{\left(3 \, t^{2}\right)}$

## F2b: Separation of variables (ver. 74)

Find the solution to the given IVP.

$y'=( -3 \, \cos\left(t\right) )y\hspace{1em} y(0)= 2$

$y= 2 \, e^{\left(-3 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 75)

Find the solution to the given IVP.

$y'=( -4 \, t + 2 )y\hspace{1em} y(0)= e^{\left(-3\right)}$

$y= e^{\left(-2 \, t^{2} + 2 \, t - 3\right)}$

## F2b: Separation of variables (ver. 76)

Find the solution to the given IVP.

$y'=( -2 \, \sin\left(t\right) )y\hspace{1em} y(0)= 3 \, e^{2}$

$y= 3 \, e^{\left(2 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 77)

Find the solution to the given IVP.

$y'=( -2 \, \cos\left(t\right) )y\hspace{1em} y(0)= 1$

$y= e^{\left(-2 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 78)

Find the solution to the given IVP.

$y'=( \sin\left(t\right) )y\hspace{1em} y(0)= 4 \, e^{\left(-1\right)}$

$y= 4 \, e^{\left(-\cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 79)

Find the solution to the given IVP.

$y'=( 2 \, \sin\left(t\right) )y\hspace{1em} y(0)= -4 \, e^{\left(-2\right)}$

$y= -4 \, e^{\left(-2 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 80)

Find the solution to the given IVP.

$y'=( 6 \, t - 3 )y\hspace{1em} y(0)= -4$

$y= -4 \, e^{\left(3 \, t^{2} - 3 \, t\right)}$

## F2b: Separation of variables (ver. 81)

Find the solution to the given IVP.

$y'=( \sin\left(t\right) )y\hspace{1em} y(0)= 2 \, e^{\left(-1\right)}$

$y= 2 \, e^{\left(-\cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 82)

Find the solution to the given IVP.

$y'=( -2 \, \sin\left(t\right) )y\hspace{1em} y(0)= -2 \, e^{2}$

$y= -2 \, e^{\left(2 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 83)

Find the solution to the given IVP.

$y'=( -\cos\left(t\right) )y\hspace{1em} y(0)= -1$

$y= -e^{\left(-\sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 84)

Find the solution to the given IVP.

$y'=( -6 \, t + 2 )y\hspace{1em} y(0)= -3 \, e^{\left(-3\right)}$

$y= -3 \, e^{\left(-3 \, t^{2} + 2 \, t - 3\right)}$

## F2b: Separation of variables (ver. 85)

Find the solution to the given IVP.

$y'=( -4 \, t + 1 )y\hspace{1em} y(0)= 2 \, e^{\left(-4\right)}$

$y= 2 \, e^{\left(-2 \, t^{2} + t - 4\right)}$

## F2b: Separation of variables (ver. 86)

Find the solution to the given IVP.

$y'=( -2 \, t - 2 )y\hspace{1em} y(0)= 3 \, e^{2}$

$y= 3 \, e^{\left(-t^{2} - 2 \, t + 2\right)}$

## F2b: Separation of variables (ver. 87)

Find the solution to the given IVP.

$y'=( 4 \, t + 2 )y\hspace{1em} y(0)= 3 \, e^{3}$

$y= 3 \, e^{\left(2 \, t^{2} + 2 \, t + 3\right)}$

## F2b: Separation of variables (ver. 88)

Find the solution to the given IVP.

$y'=( 3 \, \cos\left(t\right) )y\hspace{1em} y(0)= 2$

$y= 2 \, e^{\left(3 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 89)

Find the solution to the given IVP.

$y'=( -\sin\left(t\right) )y\hspace{1em} y(0)= -4 \, e$

$y= -4 \, e^{\cos\left(t\right)}$

## F2b: Separation of variables (ver. 90)

Find the solution to the given IVP.

$y'=( 4 \, t - 2 )y\hspace{1em} y(0)= -4 \, e^{5}$

$y= -4 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}$

## F2b: Separation of variables (ver. 91)

Find the solution to the given IVP.

$y'=( 3 \, \cos\left(t\right) )y\hspace{1em} y(0)= 1$

$y= e^{\left(3 \, \sin\left(t\right)\right)}$

## F2b: Separation of variables (ver. 92)

Find the solution to the given IVP.

$y'=( -3 \, \sin\left(t\right) )y\hspace{1em} y(0)= 3 \, e^{3}$

$y= 3 \, e^{\left(3 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 93)

Find the solution to the given IVP.

$y'=( -\sin\left(t\right) )y\hspace{1em} y(0)= -3 \, e$

$y= -3 \, e^{\cos\left(t\right)}$

## F2b: Separation of variables (ver. 94)

Find the solution to the given IVP.

$y'=( -6 \, t )y\hspace{1em} y(0)= e^{4}$

$y= e^{\left(-3 \, t^{2} + 4\right)}$

## F2b: Separation of variables (ver. 95)

Find the solution to the given IVP.

$y'=( 2 \, \sin\left(t\right) )y\hspace{1em} y(0)= 3 \, e^{\left(-2\right)}$

$y= 3 \, e^{\left(-2 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 96)

Find the solution to the given IVP.

$y'=( -\sin\left(t\right) )y\hspace{1em} y(0)= -e$

$y= -e^{\cos\left(t\right)}$

## F2b: Separation of variables (ver. 97)

Find the solution to the given IVP.

$y'=( -2 \, \sin\left(t\right) )y\hspace{1em} y(0)= 2 \, e^{2}$

$y= 2 \, e^{\left(2 \, \cos\left(t\right)\right)}$

## F2b: Separation of variables (ver. 98)

Find the solution to the given IVP.

$y'=( -2 \, t - 1 )y\hspace{1em} y(0)= 2$

$y= 2 \, e^{\left(-t^{2} - t\right)}$

## F2b: Separation of variables (ver. 99)

Find the solution to the given IVP.

$y'=( -2 \, t )y\hspace{1em} y(0)= -e^{3}$

$y= -e^{\left(-t^{2} + 3\right)}$

## F2b: Separation of variables (ver. 100)

Find the solution to the given IVP.

$y'=( 4 \, t - 3 )y\hspace{1em} y(0)= -4 \, e^{\left(-5\right)}$

$y= -4 \, e^{\left(2 \, t^{2} - 3 \, t - 5\right)}$