## F5: First order linear IVP (ver. 1)

Find the solution to the given IVP.

$-\frac{24}{t} +ty'= 5 y \hspace{1em} y( -1 ) = 3$

$y= 1 t^{ 5 } -4 \frac{1}{t}$

## F5: First order linear IVP (ver. 2)

Find the solution to the given IVP.

$-\frac{4}{t^{4}} +ty'= -5 y \hspace{1em} y( -1 ) = 6$

$y= -2 t^{ -5 } +4 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 3)

Find the solution to the given IVP.

$8 \, t +ty'= 3 y \hspace{1em} y( 1 ) = 6$

$y= 2 t^{ 3 } +4 t$

## F5: First order linear IVP (ver. 4)

Find the solution to the given IVP.

$-\frac{3}{t} +ty'= -4 y \hspace{1em} y( -1 ) = 2$

$y= 3 t^{ -4 } + \frac{1}{t}$

## F5: First order linear IVP (ver. 5)

Find the solution to the given IVP.

$-\frac{8}{t^{2}} +ty'= 2 y \hspace{1em} y( -1 ) = 0$

$y= 2 t^{ 2 } -2 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 6)

Find the solution to the given IVP.

$\frac{27}{t^{4}} +ty'= 5 y \hspace{1em} y( -1 ) = 1$

$y= 2 t^{ 5 } +3 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 7)

Find the solution to the given IVP.

$6 \, t^{3} +ty'= 5 y \hspace{1em} y( 1 ) = 7$

$y= 4 t^{ 5 } +3 t^{3}$

## F5: First order linear IVP (ver. 8)

Find the solution to the given IVP.

$\frac{40}{t^{3}} +ty'= 5 y \hspace{1em} y( 1 ) = 6$

$y= 1 t^{ 5 } +5 \frac{1}{t^{3}}$

## F5: First order linear IVP (ver. 9)

Find the solution to the given IVP.

$-24 \, t^{4} +ty'= -4 y \hspace{1em} y( 1 ) = 1$

$y= -2 t^{ -4 } +3 t^{4}$

## F5: First order linear IVP (ver. 10)

Find the solution to the given IVP.

$7 \, t^{2} +ty'= -5 y \hspace{1em} y( -1 ) = -2$

$y= 1 t^{ -5 } -1 t^{2}$

## F5: First order linear IVP (ver. 11)

Find the solution to the given IVP.

$\frac{1}{t^{2}} +ty'= -3 y \hspace{1em} y( -1 ) = 0$

$y= -1 t^{ -3 } -1 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 12)

Find the solution to the given IVP.

$5 \, t^{4} +ty'= 3 y \hspace{1em} y( -1 ) = -1$

$y= -4 t^{ 3 } -5 t^{4}$

## F5: First order linear IVP (ver. 13)

Find the solution to the given IVP.

$-\frac{10}{t^{3}} +ty'= 2 y \hspace{1em} y( -1 ) = -1$

$y= -3 t^{ 2 } -2 \frac{1}{t^{3}}$

## F5: First order linear IVP (ver. 14)

Find the solution to the given IVP.

$18 \, t^{4} +ty'= -2 y \hspace{1em} y( 1 ) = -4$

$y= -1 t^{ -2 } -3 t^{4}$

## F5: First order linear IVP (ver. 15)

Find the solution to the given IVP.

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

$y= 3 t^{ 4 } + t$

## F5: First order linear IVP (ver. 16)

Find the solution to the given IVP.

$-10 \, t +ty'= 3 y \hspace{1em} y( -1 ) = 9$

$y= -4 t^{ 3 } -5 t$

## F5: First order linear IVP (ver. 17)

Find the solution to the given IVP.

$-\frac{4}{t^{4}} +ty'= -3 y \hspace{1em} y( -1 ) = 0$

$y= -4 t^{ -3 } -4 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 18)

Find the solution to the given IVP.

$-\frac{12}{t} +ty'= -5 y \hspace{1em} y( 1 ) = 5$

$y= 2 t^{ -5 } +3 \frac{1}{t}$

## F5: First order linear IVP (ver. 19)

Find the solution to the given IVP.

$\frac{10}{t^{2}} +ty'= 3 y \hspace{1em} y( 1 ) = -1$

$y= -3 t^{ 3 } +2 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 20)

Find the solution to the given IVP.

$t^{4} +ty'= 3 y \hspace{1em} y( 1 ) = 3$

$y= 4 t^{ 3 } -1 t^{4}$

## F5: First order linear IVP (ver. 21)

Find the solution to the given IVP.

$-12 \, t^{4} +ty'= -2 y \hspace{1em} y( -1 ) = 5$

$y= 3 t^{ -2 } +2 t^{4}$

## F5: First order linear IVP (ver. 22)

Find the solution to the given IVP.

$-30 \, t^{3} +ty'= -3 y \hspace{1em} y( -1 ) = -6$

$y= 1 t^{ -3 } +5 t^{3}$

## F5: First order linear IVP (ver. 23)

Find the solution to the given IVP.

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

$y= 2 t^{ -2 } + t$

## F5: First order linear IVP (ver. 24)

Find the solution to the given IVP.

$-\frac{10}{t^{2}} +ty'= 3 y \hspace{1em} y( -1 ) = -5$

$y= 3 t^{ 3 } -2 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 25)

Find the solution to the given IVP.

$-\frac{20}{t} +ty'= 3 y \hspace{1em} y( 1 ) = -8$

$y= -3 t^{ 3 } -5 \frac{1}{t}$

## F5: First order linear IVP (ver. 26)

Find the solution to the given IVP.

$\frac{45}{t^{4}} +ty'= 5 y \hspace{1em} y( -1 ) = 2$

$y= 3 t^{ 5 } +5 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 27)

Find the solution to the given IVP.

$-\frac{16}{t^{2}} +ty'= 2 y \hspace{1em} y( 1 ) = -6$

$y= -2 t^{ 2 } -4 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 28)

Find the solution to the given IVP.

$\frac{24}{t^{3}} +ty'= 3 y \hspace{1em} y( 1 ) = 2$

$y= -2 t^{ 3 } +4 \frac{1}{t^{3}}$

## F5: First order linear IVP (ver. 29)

Find the solution to the given IVP.

$-\frac{24}{t^{3}} +ty'= 5 y \hspace{1em} y( -1 ) = 2$

$y= 1 t^{ 5 } -3 \frac{1}{t^{3}}$

## F5: First order linear IVP (ver. 30)

Find the solution to the given IVP.

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

$y= 3 t^{ 3 } + t$

## F5: First order linear IVP (ver. 31)

Find the solution to the given IVP.

$-\frac{12}{t^{2}} +ty'= 2 y \hspace{1em} y( 1 ) = -2$

$y= 1 t^{ 2 } -3 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 32)

Find the solution to the given IVP.

$\frac{35}{t^{3}} +ty'= 4 y \hspace{1em} y( 1 ) = 1$

$y= -4 t^{ 4 } +5 \frac{1}{t^{3}}$

## F5: First order linear IVP (ver. 33)

Find the solution to the given IVP.

$-24 \, t^{4} +ty'= -2 y \hspace{1em} y( 1 ) = 0$

$y= -4 t^{ -2 } +4 t^{4}$

## F5: First order linear IVP (ver. 34)

Find the solution to the given IVP.

$-\frac{30}{t^{2}} +ty'= 4 y \hspace{1em} y( -1 ) = -3$

$y= 2 t^{ 4 } -5 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 35)

Find the solution to the given IVP.

$\frac{35}{t^{4}} +ty'= 3 y \hspace{1em} y( 1 ) = 9$

$y= 4 t^{ 3 } +5 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 36)

Find the solution to the given IVP.

$\frac{1}{t^{4}} +ty'= -5 y \hspace{1em} y( 1 ) = -2$

$y= -1 t^{ -5 } -1 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 37)

Find the solution to the given IVP.

$-\frac{24}{t^{3}} +ty'= 5 y \hspace{1em} y( 1 ) = -5$

$y= -2 t^{ 5 } -3 \frac{1}{t^{3}}$

## F5: First order linear IVP (ver. 38)

Find the solution to the given IVP.

$\frac{5}{t} +ty'= -2 y \hspace{1em} y( -1 ) = 2$

$y= -3 t^{ -2 } -5 \frac{1}{t}$

## F5: First order linear IVP (ver. 39)

Find the solution to the given IVP.

$-\frac{6}{t^{2}} +ty'= -5 y \hspace{1em} y( 1 ) = 0$

$y= -2 t^{ -5 } +2 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 40)

Find the solution to the given IVP.

$20 \, t^{2} +ty'= -3 y \hspace{1em} y( -1 ) = -5$

$y= 1 t^{ -3 } -4 t^{2}$

## F5: First order linear IVP (ver. 41)

Find the solution to the given IVP.

$-5 \, t^{4} +ty'= 3 y \hspace{1em} y( 1 ) = 4$

$y= -1 t^{ 3 } +5 t^{4}$

## F5: First order linear IVP (ver. 42)

Find the solution to the given IVP.

$-\frac{8}{t} +ty'= 3 y \hspace{1em} y( 1 ) = -5$

$y= -3 t^{ 3 } -2 \frac{1}{t}$

## F5: First order linear IVP (ver. 43)

Find the solution to the given IVP.

$\frac{30}{t^{4}} +ty'= 2 y \hspace{1em} y( -1 ) = 8$

$y= 3 t^{ 2 } +5 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 44)

Find the solution to the given IVP.

$-\frac{2}{t} +ty'= -2 y \hspace{1em} y( -1 ) = -1$

$y= 1 t^{ -2 } +2 \frac{1}{t}$

## F5: First order linear IVP (ver. 45)

Find the solution to the given IVP.

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

$y= -3 t^{ 5 } -2 t^{4}$

## F5: First order linear IVP (ver. 46)

Find the solution to the given IVP.

$-\frac{7}{t^{4}} +ty'= 3 y \hspace{1em} y( -1 ) = -3$

$y= 2 t^{ 3 } -1 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 47)

Find the solution to the given IVP.

$\frac{2}{t^{4}} +ty'= -5 y \hspace{1em} y( -1 ) = 0$

$y= -2 t^{ -5 } -2 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 48)

Find the solution to the given IVP.

$-\frac{16}{t^{2}} +ty'= 2 y \hspace{1em} y( 1 ) = 0$

$y= 4 t^{ 2 } -4 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 49)

Find the solution to the given IVP.

$-25 \, t^{2} +ty'= -3 y \hspace{1em} y( -1 ) = 7$

$y= -2 t^{ -3 } +5 t^{2}$

## F5: First order linear IVP (ver. 50)

Find the solution to the given IVP.

$14 \, t^{3} +ty'= -4 y \hspace{1em} y( 1 ) = -5$

$y= -3 t^{ -4 } -2 t^{3}$

## F5: First order linear IVP (ver. 51)

Find the solution to the given IVP.

$25 \, t^{2} +ty'= -3 y \hspace{1em} y( 1 ) = -2$

$y= 3 t^{ -3 } -5 t^{2}$

## F5: First order linear IVP (ver. 52)

Find the solution to the given IVP.

$\frac{12}{t} +ty'= 3 y \hspace{1em} y( 1 ) = 7$

$y= 4 t^{ 3 } +3 \frac{1}{t}$

## F5: First order linear IVP (ver. 53)

Find the solution to the given IVP.

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

$y= 1 t^{ 4 } + t^{3}$

## F5: First order linear IVP (ver. 54)

Find the solution to the given IVP.

$t^{3} +ty'= 4 y \hspace{1em} y( 1 ) = 4$

$y= 3 t^{ 4 } + t^{3}$

## F5: First order linear IVP (ver. 55)

Find the solution to the given IVP.

$9 \, t^{2} +ty'= 5 y \hspace{1em} y( -1 ) = 1$

$y= 2 t^{ 5 } +3 t^{2}$

## F5: First order linear IVP (ver. 56)

Find the solution to the given IVP.

$\frac{8}{t^{2}} +ty'= -4 y \hspace{1em} y( 1 ) = -7$

$y= -3 t^{ -4 } -4 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 57)

Find the solution to the given IVP.

$-28 \, t^{3} +ty'= -4 y \hspace{1em} y( 1 ) = 7$

$y= 3 t^{ -4 } +4 t^{3}$

## F5: First order linear IVP (ver. 58)

Find the solution to the given IVP.

$5 \, t +ty'= -4 y \hspace{1em} y( -1 ) = 0$

$y= -1 t^{ -4 } -1 t$

## F5: First order linear IVP (ver. 59)

Find the solution to the given IVP.

$8 \, t^{2} +ty'= -2 y \hspace{1em} y( 1 ) = 0$

$y= 2 t^{ -2 } -2 t^{2}$

## F5: First order linear IVP (ver. 60)

Find the solution to the given IVP.

$-\frac{10}{t} +ty'= -3 y \hspace{1em} y( -1 ) = -7$

$y= 2 t^{ -3 } +5 \frac{1}{t}$

## F5: First order linear IVP (ver. 61)

Find the solution to the given IVP.

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

$y= 4 t^{ 2 } -3 t^{4}$

## F5: First order linear IVP (ver. 62)

Find the solution to the given IVP.

$-\frac{4}{t^{4}} +ty'= -2 y \hspace{1em} y( -1 ) = -5$

$y= -3 t^{ -2 } -2 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 63)

Find the solution to the given IVP.

$\frac{6}{t^{2}} +ty'= -5 y \hspace{1em} y( -1 ) = 1$

$y= -3 t^{ -5 } -2 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 64)

Find the solution to the given IVP.

$-\frac{28}{t^{2}} +ty'= 5 y \hspace{1em} y( -1 ) = 0$

$y= -4 t^{ 5 } -4 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 65)

Find the solution to the given IVP.

$-\frac{20}{t} +ty'= -5 y \hspace{1em} y( 1 ) = 7$

$y= 2 t^{ -5 } +5 \frac{1}{t}$

## F5: First order linear IVP (ver. 66)

Find the solution to the given IVP.

$18 \, t^{3} +ty'= -3 y \hspace{1em} y( 1 ) = -4$

$y= -1 t^{ -3 } -3 t^{3}$

## F5: First order linear IVP (ver. 67)

Find the solution to the given IVP.

$\frac{9}{t^{4}} +ty'= 5 y \hspace{1em} y( 1 ) = 2$

$y= 1 t^{ 5 } + \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 68)

Find the solution to the given IVP.

$-8 \, t^{4} +ty'= 2 y \hspace{1em} y( 1 ) = 1$

$y= -3 t^{ 2 } +4 t^{4}$

## F5: First order linear IVP (ver. 69)

Find the solution to the given IVP.

$-\frac{7}{t^{4}} +ty'= 3 y \hspace{1em} y( -1 ) = -2$

$y= 1 t^{ 3 } -1 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 70)

Find the solution to the given IVP.

$\frac{8}{t^{3}} +ty'= -5 y \hspace{1em} y( -1 ) = 8$

$y= -4 t^{ -5 } -4 \frac{1}{t^{3}}$

## F5: First order linear IVP (ver. 71)

Find the solution to the given IVP.

$-8 \, t^{3} +ty'= -5 y \hspace{1em} y( 1 ) = 0$

$y= -1 t^{ -5 } + t^{3}$

## F5: First order linear IVP (ver. 72)

Find the solution to the given IVP.

$-\frac{18}{t} +ty'= 5 y \hspace{1em} y( 1 ) = -4$

$y= -1 t^{ 5 } -3 \frac{1}{t}$

## F5: First order linear IVP (ver. 73)

Find the solution to the given IVP.

$-\frac{32}{t^{4}} +ty'= 4 y \hspace{1em} y( -1 ) = -7$

$y= -3 t^{ 4 } -4 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 74)

Find the solution to the given IVP.

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

$y= 1 t^{ 2 } +3 t$

## F5: First order linear IVP (ver. 75)

Find the solution to the given IVP.

$-\frac{3}{t^{4}} +ty'= -3 y \hspace{1em} y( 1 ) = -1$

$y= 2 t^{ -3 } -3 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 76)

Find the solution to the given IVP.

$\frac{45}{t^{4}} +ty'= 5 y \hspace{1em} y( 1 ) = 2$

$y= -3 t^{ 5 } +5 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 77)

Find the solution to the given IVP.

$-4 \, t +ty'= 5 y \hspace{1em} y( 1 ) = 3$

$y= 4 t^{ 5 } -1 t$

## F5: First order linear IVP (ver. 78)

Find the solution to the given IVP.

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

$y= -1 t^{ 2 } +2 t^{4}$

## F5: First order linear IVP (ver. 79)

Find the solution to the given IVP.

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

$y= 1 t^{ -3 } -1 t$

## F5: First order linear IVP (ver. 80)

Find the solution to the given IVP.

$\frac{45}{t^{4}} +ty'= 5 y \hspace{1em} y( -1 ) = 7$

$y= -2 t^{ 5 } +5 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 81)

Find the solution to the given IVP.

$7 \, t^{2} +ty'= -5 y \hspace{1em} y( 1 ) = -2$

$y= -1 t^{ -5 } -1 t^{2}$

## F5: First order linear IVP (ver. 82)

Find the solution to the given IVP.

$\frac{5}{t^{4}} +ty'= -5 y \hspace{1em} y( -1 ) = -7$

$y= 2 t^{ -5 } -5 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 83)

Find the solution to the given IVP.

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

$y= -2 t^{ -2 } -1 t^{2}$

## F5: First order linear IVP (ver. 84)

Find the solution to the given IVP.

$\frac{6}{t^{2}} +ty'= -4 y \hspace{1em} y( 1 ) = -4$

$y= -1 t^{ -4 } -3 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 85)

Find the solution to the given IVP.

$-\frac{10}{t} +ty'= -3 y \hspace{1em} y( 1 ) = 6$

$y= 1 t^{ -3 } +5 \frac{1}{t}$

## F5: First order linear IVP (ver. 86)

Find the solution to the given IVP.

$-24 \, t^{3} +ty'= -3 y \hspace{1em} y( -1 ) = -7$

$y= 3 t^{ -3 } +4 t^{3}$

## F5: First order linear IVP (ver. 87)

Find the solution to the given IVP.

$-\frac{6}{t^{3}} +ty'= 3 y \hspace{1em} y( 1 ) = 2$

$y= 3 t^{ 3 } -1 \frac{1}{t^{3}}$

## F5: First order linear IVP (ver. 88)

Find the solution to the given IVP.

$-40 \, t^{3} +ty'= -5 y \hspace{1em} y( -1 ) = -9$

$y= 4 t^{ -5 } +5 t^{3}$

## F5: First order linear IVP (ver. 89)

Find the solution to the given IVP.

$32 \, t^{3} +ty'= -5 y \hspace{1em} y( 1 ) = -7$

$y= -3 t^{ -5 } -4 t^{3}$

## F5: First order linear IVP (ver. 90)

Find the solution to the given IVP.

$\frac{10}{t^{2}} +ty'= 3 y \hspace{1em} y( -1 ) = 6$

$y= -4 t^{ 3 } +2 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 91)

Find the solution to the given IVP.

$-28 \, t^{3} +ty'= -4 y \hspace{1em} y( 1 ) = 6$

$y= 2 t^{ -4 } +4 t^{3}$

## F5: First order linear IVP (ver. 92)

Find the solution to the given IVP.

$-\frac{24}{t^{4}} +ty'= 2 y \hspace{1em} y( -1 ) = -3$

$y= 1 t^{ 2 } -4 \frac{1}{t^{4}}$

## F5: First order linear IVP (ver. 93)

Find the solution to the given IVP.

$-\frac{25}{t^{3}} +ty'= 2 y \hspace{1em} y( 1 ) = -7$

$y= -2 t^{ 2 } -5 \frac{1}{t^{3}}$

## F5: First order linear IVP (ver. 94)

Find the solution to the given IVP.

$-\frac{6}{t^{2}} +ty'= -4 y \hspace{1em} y( 1 ) = -1$

$y= -4 t^{ -4 } +3 \frac{1}{t^{2}}$

## F5: First order linear IVP (ver. 95)

Find the solution to the given IVP.

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

$y= 1 t^{ 3 } +3 t$

## F5: First order linear IVP (ver. 96)

Find the solution to the given IVP.

$12 \, t +ty'= 4 y \hspace{1em} y( -1 ) = -8$

$y= -4 t^{ 4 } +4 t$

## F5: First order linear IVP (ver. 97)

Find the solution to the given IVP.

$-\frac{4}{t^{3}} +ty'= -2 y \hspace{1em} y( 1 ) = -1$

$y= 3 t^{ -2 } -4 \frac{1}{t^{3}}$

## F5: First order linear IVP (ver. 98)

Find the solution to the given IVP.

$\frac{1}{t^{3}} +ty'= -2 y \hspace{1em} y( -1 ) = 1$

$y= 2 t^{ -2 } + \frac{1}{t^{3}}$

## F5: First order linear IVP (ver. 99)

Find the solution to the given IVP.

$-\frac{3}{t} +ty'= -2 y \hspace{1em} y( -1 ) = 1$

$y= 4 t^{ -2 } +3 \frac{1}{t}$

## F5: First order linear IVP (ver. 100)

Find the solution to the given IVP.

$-\frac{14}{t^{4}} +ty'= 3 y \hspace{1em} y( -1 ) = -1$

$y= -1 t^{ 3 } -2 \frac{1}{t^{4}}$