What is the solution for (d^2y)/(dt^2)+9y=0 ?

The solution for (d^2y)/(dt^2)+9y=0 is y=c_{1}cos(3t)+c_{2}sin(3t)

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(d^2y)/(dt^2)+9y=0

\frac{d ^{2} y}{d t ^{2}} + 9 y = 0

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

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 9 y = 0

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)

y^{^{''}} + 81 y = 0, y (0) = 4, y^{^{'}} (0) = 1

4 y^{^{''}} - 12 y^{^{'}} + 10 y = 0

y^{^{''}} + 5 y^{^{'}} + 13 y = 0

y^{^{''}} + 10 y^{^{'}} + 23 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + 15 y^{^{'}} + 50 y = 0, y (0) = 8, y^{^{'}} (0) = - 55

What is the solution for (d^2y)/(dt^2)+9y=0 ?
The solution for (d^2y)/(dt^2)+9y=0 is y=c_{1}cos(3t)+c_{2}sin(3t)