What is the solution for y^{''}+81y=8sin(9t) ?

The solution for y^{''}+81y=8sin(9t) is y=c_{1}cos(9t)+c_{2}sin(9t)-(4tcos(9t))/9

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y^{''}+81y=8sin(9t)

y^{^{''}} + 81 y = 8 sin (9 t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) - \frac{4 t cos ( 9 t )}{9}

Solution steps

y^{''} (t) + 81 y = 8 sin (9 t)

Solve linear ODE:

y = c_{1} cos (9 t) + c_{2} sin (9 t) - \frac{4 t cos ( 9 t )}{9}

y = c_{1} cos (9 t) + c_{2} sin (9 t) - \frac{4 t cos ( 9 t )}{9}

x^{^{''}} + 2 x^{^{'}} + 5 x = 5 cos (t)

y^{^{''}} + 4 y = 4 csc^{2} (2 x)

y^{^{''}} + 2 y^{^{'}} - 3 y = sin (2 t)

y^{^{''}} + 4 y^{^{'}} + 2 y = x e^{- 2 x}

y^{^{''}} + 10 y^{^{'}} + 25 y = e^{- 5 t} ln (t)

What is the solution for y^{''}+81y=8sin(9t) ?
The solution for y^{''}+81y=8sin(9t) is y=c_{1}cos(9t)+c_{2}sin(9t)-(4tcos(9t))/9