What is the solution for (d^2x)/(dt^2)+100x=36cos(8t) ?

The solution for (d^2x)/(dt^2)+100x=36cos(8t) is x=c_{1}cos(10t)+c_{2}sin(10t)+cos(8t)

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(d^2x)/(dt^2)+100x=36cos(8t)

\frac{d ^{2} x}{d t ^{2}} + 100 x = 36 cos (8 t)

x = c_{1} cos (10 t) + c_{2} sin (10 t) + cos (8 t)

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 100 x = 36 cos (8 t)

Solve linear ODE:

x = c_{1} cos (10 t) + c_{2} sin (10 t) + cos (8 t)

x = c_{1} cos (10 t) + c_{2} sin (10 t) + cos (8 t)

What is the solution for (d^2x)/(dt^2)+100x=36cos(8t) ?
The solution for (d^2x)/(dt^2)+100x=36cos(8t) is x=c_{1}cos(10t)+c_{2}sin(10t)+cos(8t)