What is the solution for y^{''}+81y=sin(9t) ?

The solution for y^{''}+81y=sin(9t) is y=c_{1}cos(9t)+c_{2}sin(9t)-(tcos(9t))/(18)

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y^{''}+81y=sin(9t)

y^{^{''}} + 81 y = sin (9 t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) - \frac{t cos ( 9 t )}{18}

Solution steps

y^{''} (t) + 81 y = sin (9 t)

Solve linear ODE:

y = c_{1} cos (9 t) + c_{2} sin (9 t) - \frac{t cos ( 9 t )}{18}

y = c_{1} cos (9 t) + c_{2} sin (9 t) - \frac{t cos ( 9 t )}{18}

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What is the solution for y^{''}+81y=sin(9t) ?
The solution for y^{''}+81y=sin(9t) is y=c_{1}cos(9t)+c_{2}sin(9t)-(tcos(9t))/(18)