What is the solution for y^{''}+36y=sin(9x) ?

The solution for y^{''}+36y=sin(9x) is y=c_{1}cos(6x)+c_{2}sin(6x)-1/45 sin(9x)

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y^{''}+36y=sin(9x)

y^{^{''}} + 36 y = sin (9 x)

y = c_{1} cos (6 x) + c_{2} sin (6 x) - \frac{1}{45} sin (9 x)

Solution steps

y^{''} (x) + 36 y = sin (9 x)

Solve linear ODE:

y = c_{1} cos (6 x) + c_{2} sin (6 x) - \frac{1}{45} sin (9 x)

y = c_{1} cos (6 x) + c_{2} sin (6 x) - \frac{1}{45} sin (9 x)

What is the solution for y^{''}+36y=sin(9x) ?
The solution for y^{''}+36y=sin(9x) is y=c_{1}cos(6x)+c_{2}sin(6x)-1/45 sin(9x)