## C5b - Homogeneous second-order linear IVP (ver. 1)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -1 , y'(0) = 4$

$y= -\cos\left(4 \, t\right) + \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 2)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -4 , y'(0) = -4$

$y= -4 \, \cos\left(4 \, t\right) - \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 3)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 3 , y'(0) = 12$

$y= 3 \, \cos\left(3 \, t\right) + 4 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 4)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = -4 , y'(0) = -6$

$y= -4 \, \cos\left(3 \, t\right) - 2 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 5)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -3 , y'(0) = 0$

$y= -3 \, \cos\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 6)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -2 , y'(0) = 16$

$y= -2 \, \cos\left(4 \, t\right) + 4 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 7)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 0 , y'(0) = 12$

$y= 3 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 8)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 1 , y'(0) = 20$

$y= \cos\left(4 \, t\right) + 5 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 9)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 1 , y'(0) = -6$

$y= \cos\left(3 \, t\right) - 2 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 10)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -5 , y'(0) = -4$

$y= -5 \, \cos\left(4 \, t\right) - \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 11)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = -4 , y'(0) = 0$

$y= -4 \, \cos\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 12)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 0 , y'(0) = 3$

$y= \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 13)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -4 , y'(0) = 8$

$y= -4 \, \cos\left(2 \, t\right) + 4 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 14)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 4 , y'(0) = -8$

$y= 4 \, \cos\left(2 \, t\right) - 4 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 15)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -3 , y'(0) = 8$

$y= -3 \, \cos\left(4 \, t\right) + 2 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 16)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = -5 , y'(0) = 3$

$y= -5 \, \cos\left(3 \, t\right) + \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 17)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 0 , y'(0) = -3$

$y= -\sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 18)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 1 , y'(0) = -4$

$y= \cos\left(4 \, t\right) - \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 19)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 0 , y'(0) = 15$

$y= 5 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 20)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 1 , y'(0) = 6$

$y= \cos\left(3 \, t\right) + 2 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 21)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -3 , y'(0) = -10$

$y= -3 \, \cos\left(2 \, t\right) - 5 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 22)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -4 , y'(0) = 0$

$y= -4 \, \cos\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 23)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -2 , y'(0) = -8$

$y= -2 \, \cos\left(2 \, t\right) - 4 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 24)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = -2 , y'(0) = 12$

$y= -2 \, \cos\left(3 \, t\right) + 4 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 25)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 5 , y'(0) = 9$

$y= 5 \, \cos\left(3 \, t\right) + 3 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 26)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -5 , y'(0) = 12$

$y= -5 \, \cos\left(4 \, t\right) + 3 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 27)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 5 , y'(0) = 6$

$y= 5 \, \cos\left(2 \, t\right) + 3 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 28)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 3 , y'(0) = 15$

$y= 3 \, \cos\left(3 \, t\right) + 5 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 29)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -2 , y'(0) = 4$

$y= -2 \, \cos\left(4 \, t\right) + \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 30)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = -5 , y'(0) = 9$

$y= -5 \, \cos\left(3 \, t\right) + 3 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 31)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 1 , y'(0) = 4$

$y= \cos\left(2 \, t\right) + 2 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 32)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 3 , y'(0) = 3$

$y= 3 \, \cos\left(3 \, t\right) + \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 33)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 3 , y'(0) = -2$

$y= 3 \, \cos\left(2 \, t\right) - \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 34)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = -2 , y'(0) = 12$

$y= -2 \, \cos\left(3 \, t\right) + 4 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 35)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 0 , y'(0) = 8$

$y= 4 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 36)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 0 , y'(0) = -4$

$y= -\sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 37)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 5 , y'(0) = 8$

$y= 5 \, \cos\left(4 \, t\right) + 2 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 38)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -5 , y'(0) = -6$

$y= -5 \, \cos\left(2 \, t\right) - 3 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 39)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 2 , y'(0) = -12$

$y= 2 \, \cos\left(4 \, t\right) - 3 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 40)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = -4 , y'(0) = -6$

$y= -4 \, \cos\left(3 \, t\right) - 2 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 41)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 4 , y'(0) = 10$

$y= 4 \, \cos\left(2 \, t\right) + 5 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 42)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 3 , y'(0) = 12$

$y= 3 \, \cos\left(3 \, t\right) + 4 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 43)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -1 , y'(0) = 4$

$y= -\cos\left(2 \, t\right) + 2 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 44)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 1 , y'(0) = -10$

$y= \cos\left(2 \, t\right) - 5 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 45)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -5 , y'(0) = 4$

$y= -5 \, \cos\left(4 \, t\right) + \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 46)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = -1 , y'(0) = 9$

$y= -\cos\left(3 \, t\right) + 3 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 47)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -5 , y'(0) = -8$

$y= -5 \, \cos\left(4 \, t\right) - 2 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 48)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 2 , y'(0) = 0$

$y= 2 \, \cos\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 49)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = -1 , y'(0) = -9$

$y= -\cos\left(3 \, t\right) - 3 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 50)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 4 , y'(0) = -15$

$y= 4 \, \cos\left(3 \, t\right) - 5 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 51)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 1 , y'(0) = -4$

$y= \cos\left(2 \, t\right) - 2 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 52)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 1 , y'(0) = 12$

$y= \cos\left(3 \, t\right) + 4 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 53)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 4 , y'(0) = 4$

$y= 4 \, \cos\left(4 \, t\right) + \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 54)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 0 , y'(0) = 8$

$y= 2 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 55)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -4 , y'(0) = 16$

$y= -4 \, \cos\left(4 \, t\right) + 4 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 56)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 3 , y'(0) = -9$

$y= 3 \, \cos\left(3 \, t\right) - 3 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 57)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 3 , y'(0) = -12$

$y= 3 \, \cos\left(4 \, t\right) - 3 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 58)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = -2 , y'(0) = -3$

$y= -2 \, \cos\left(3 \, t\right) - \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 59)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 3 , y'(0) = -10$

$y= 3 \, \cos\left(2 \, t\right) - 5 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 60)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -5 , y'(0) = -4$

$y= -5 \, \cos\left(2 \, t\right) - 2 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 61)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -2 , y'(0) = 10$

$y= -2 \, \cos\left(2 \, t\right) + 5 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 62)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -3 , y'(0) = -2$

$y= -3 \, \cos\left(2 \, t\right) - \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 63)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -3 , y'(0) = -16$

$y= -3 \, \cos\left(4 \, t\right) - 4 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 64)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -5 , y'(0) = 8$

$y= -5 \, \cos\left(4 \, t\right) + 2 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 65)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 1 , y'(0) = -8$

$y= \cos\left(4 \, t\right) - 2 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 66)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 4 , y'(0) = -12$

$y= 4 \, \cos\left(3 \, t\right) - 4 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 67)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 4 , y'(0) = 20$

$y= 4 \, \cos\left(4 \, t\right) + 5 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 68)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 1 , y'(0) = 8$

$y= \cos\left(2 \, t\right) + 4 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 69)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 0 , y'(0) = 3$

$y= \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 70)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -4 , y'(0) = -8$

$y= -4 \, \cos\left(4 \, t\right) - 2 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 71)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 5 , y'(0) = -4$

$y= 5 \, \cos\left(4 \, t\right) - \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 72)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 2 , y'(0) = 16$

$y= 2 \, \cos\left(4 \, t\right) + 4 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 73)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -2 , y'(0) = 0$

$y= -2 \, \cos\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 74)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 0 , y'(0) = 4$

$y= 2 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 75)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 3 , y'(0) = -3$

$y= 3 \, \cos\left(3 \, t\right) - \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 76)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 3 , y'(0) = 4$

$y= 3 \, \cos\left(4 \, t\right) + \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 77)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 5 , y'(0) = 16$

$y= 5 \, \cos\left(4 \, t\right) + 4 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 78)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 2 , y'(0) = 10$

$y= 2 \, \cos\left(2 \, t\right) + 5 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 79)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -3 , y'(0) = -4$

$y= -3 \, \cos\left(2 \, t\right) - 2 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 80)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -5 , y'(0) = 16$

$y= -5 \, \cos\left(4 \, t\right) + 4 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 81)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 3 , y'(0) = -16$

$y= 3 \, \cos\left(4 \, t\right) - 4 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 82)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -1 , y'(0) = -12$

$y= -\cos\left(4 \, t\right) - 3 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 83)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -1 , y'(0) = -10$

$y= -\cos\left(2 \, t\right) - 5 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 84)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 2 , y'(0) = 0$

$y= 2 \, \cos\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 85)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 2 , y'(0) = 0$

$y= 2 \, \cos\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 86)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -3 , y'(0) = -10$

$y= -3 \, \cos\left(2 \, t\right) - 5 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 87)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = 3 , y'(0) = 15$

$y= 3 \, \cos\left(3 \, t\right) + 5 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 88)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -2 , y'(0) = -12$

$y= -2 \, \cos\left(4 \, t\right) - 3 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 89)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 1 , y'(0) = -12$

$y= \cos\left(4 \, t\right) - 3 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 90)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = -4 , y'(0) = 15$

$y= -4 \, \cos\left(3 \, t\right) + 5 \, \sin\left(3 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 91)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 1 , y'(0) = -20$

$y= \cos\left(4 \, t\right) - 5 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 92)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -4 , y'(0) = 4$

$y= -4 \, \cos\left(2 \, t\right) + 2 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 93)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 3 , y'(0) = 0$

$y= 3 \, \cos\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 94)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = 0 , y'(0) = -12$

$y= -3 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 95)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 3 , y'(0) = 8$

$y= 3 \, \cos\left(2 \, t\right) + 4 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 96)

Find the solution to the given IVP.

$y''+16y = 0 \hspace{1em} y(0) = -1 , y'(0) = 8$

$y= -\cos\left(4 \, t\right) + 2 \, \sin\left(4 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 97)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 4 , y'(0) = 0$

$y= 4 \, \cos\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 98)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = -2 , y'(0) = -10$

$y= -2 \, \cos\left(2 \, t\right) - 5 \, \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 99)

Find the solution to the given IVP.

$y''+4y = 0 \hspace{1em} y(0) = 3 , y'(0) = -2$

$y= 3 \, \cos\left(2 \, t\right) - \sin\left(2 \, t\right)$

## C5b - Homogeneous second-order linear IVP (ver. 100)

Find the solution to the given IVP.

$y''+9y = 0 \hspace{1em} y(0) = -4 , y'(0) = 3$

$y= -4 \, \cos\left(3 \, t\right) + \sin\left(3 \, t\right)$