What is the solution for (d^2x)/(dt^2)+81x=8sin(9t) ?

The solution for (d^2x)/(dt^2)+81x=8sin(9t) is x=c_{1}cos(9t)+c_{2}sin(9t)-(4tcos(9t))/9

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(d^2x)/(dt^2)+81x=8sin(9t)

\frac{d ^{2} x}{d t ^{2}} + 81 x = 8 sin (9 t)

x = c_{1} cos (9 t) + c_{2} sin (9 t) - \frac{4 t cos ( 9 t )}{9}

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 81 x = 8 sin (9 t)

Solve linear ODE:

x = c_{1} cos (9 t) + c_{2} sin (9 t) - \frac{4 t cos ( 9 t )}{9}

x = c_{1} cos (9 t) + c_{2} sin (9 t) - \frac{4 t cos ( 9 t )}{9}

What is the solution for (d^2x)/(dt^2)+81x=8sin(9t) ?
The solution for (d^2x)/(dt^2)+81x=8sin(9t) is x=c_{1}cos(9t)+c_{2}sin(9t)-(4tcos(9t))/9