What is the solution for (d^2y)/(dx^2)+9y=sin(3x) ?

The solution for (d^2y)/(dx^2)+9y=sin(3x) is y=c_{1}cos(3x)+c_{2}sin(3x)-(xcos(3x))/6

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(d^2y)/(dx^2)+9y=sin(3x)

\frac{d ^{2} y}{d x ^{2}} + 9 y = sin (3 x)

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 9 y = sin (3 x)

Solve linear ODE:

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

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

What is the solution for (d^2y)/(dx^2)+9y=sin(3x) ?
The solution for (d^2y)/(dx^2)+9y=sin(3x) is y=c_{1}cos(3x)+c_{2}sin(3x)-(xcos(3x))/6