What is the solution for (d^2y)/(dt^2)=-9y ?

The solution for (d^2y)/(dt^2)=-9y is y=c_{1}cos(3t)+c_{2}sin(3t)

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(d^2y)/(dt^2)=-9y

\frac{d ^{2} y}{d t ^{2}} = - 9 y

y = c_{1} cos (3 t) + c_{2} sin (3 t)

Solution steps

\frac{d ^{2} y}{d t ^{2}} = - 9 y

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t)

f^{^{''}} (t) + f (t) = 0

y^{^{''}} - 6 y^{^{'}} = 0, y (0) = 5 - 5 e^{6}, y (1) = 0

y^{^{''}} - 8 y^{^{'}} + 5 y = 0

1 x^{^{''}} + 6 x^{^{'}} - 1 x = 0

6 y^{^{''''}} + 77 y^{^{''}} + 25 y = 0

What is the solution for (d^2y)/(dt^2)=-9y ?
The solution for (d^2y)/(dt^2)=-9y is y=c_{1}cos(3t)+c_{2}sin(3t)