What is the solution for (d^2y)/(dt^2)+9y=cos(3t) ?

The solution for (d^2y)/(dt^2)+9y=cos(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)+(tsin(3t))/6

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(d^2y)/(dt^2)+9y=cos(3t)

\frac{d ^{2} y}{d t ^{2}} + 9 y = cos (3 t)

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{t sin ( 3 t )}{6}

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 9 y = cos (3 t)

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{t sin ( 3 t )}{6}

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{t sin ( 3 t )}{6}

What is the solution for (d^2y)/(dt^2)+9y=cos(3t) ?
The solution for (d^2y)/(dt^2)+9y=cos(3t) is y=c_{1}cos(3t)+c_{2}sin(3t)+(tsin(3t))/6