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

The solution for (d^2x)/(dt^2)+ax=0 is x=c_{1}cos(sqrt(a)t)+c_{2}sin(sqrt(a)t)

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(d^2x)/(dt^2)+ax=0

\frac{d ^{2} x}{d t ^{2}} + a x = 0

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

Solution steps

\frac{d ^{2} x}{d t ^{2}} + a x (t) = 0

Solve linear ODE:

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

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

\frac{d}{d x} (1 - 2 x + 3 x^{2} - 4 x^{3})

\int e^{0.2 x} d x

y^{^{''}} - 9 y^{^{'}} = 81 t, y (0) = 9, y^{^{'}} (0) = 0

\int \frac{- 3}{7 e ^{7 x}} d x

\frac{d}{d x} (\frac{2}{e ^{x} - e ^{- x}})

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