What is the solution for (d^2y)/(dt^2)+4y=0 ?

The solution for (d^2y)/(dt^2)+4y=0 is y=c_{1}cos(2t)+c_{2}sin(2t)

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(d^2y)/(dt^2)+4y=0

\frac{d ^{2} y}{d t ^{2}} + 4 y = 0

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

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 4 y = 0

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 0

- 2 y^{^{''}} + 5 y^{^{'}} + 10 y = 0

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = 2, y^{^{'}} (0) = 16

100 y^{^{''}} + 180 y^{^{'}} + 145 y = 0

y^{^{''}} + 4 y = 0, y (0) = 5, y^{^{'}} (0) = - 3

What is the solution for (d^2y)/(dt^2)+4y=0 ?
The solution for (d^2y)/(dt^2)+4y=0 is y=c_{1}cos(2t)+c_{2}sin(2t)