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

The solution for (d^2x)/(dt^2)+k^2x=0 is x=c_{1}cos(kt)+c_{2}sin(kt)

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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