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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

(D^{2} - 1) y = e^{- x} (2 sin (x) + 4 cos (x))

\frac{d ^{2} y}{d x ^{2}} - y = x \cdot e^{2 x}

y^{^{''}} + 4 y^{^{'}} + 4 y = 5 x + 4 - e^{5 x}

y^{^{''}} - 6 y^{^{'}} + 5 y = 34 sin (3 t)

y^{^{''}} - 9 y^{^{'}} + 2 y = t e^{t}

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