What is the solution for (d^2x)/(dt^2)=-4x ?

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

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(d^2x)/(dt^2)=-4x

\frac{d ^{2} x}{d t ^{2}} = - 4 x

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

Solution steps

\frac{d ^{2} x}{d t ^{2}} = - 4 x

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 12 y = 0

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 37 y = 0

25 x^{^{''}} + 50 x^{^{'}} + 169 x = 0, x (0) = 3, x^{^{'}} (0) = 14

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 4, y^{^{'}} (0) = 6

y^{^{''}} + 128 y = 0

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