What is the solution for 4y^{''}+324y=8sin(t) ?

The solution for 4y^{''}+324y=8sin(t) is y=c_{1}cos(9t)+c_{2}sin(9t)+1/40 sin(t)

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4y^{''}+324y=8sin(t)

4 y^{^{''}} + 324 y = 8 sin (t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{40} sin (t)

Solution steps

4 y^{''} (t) + 324 y = 8 sin (t)

Solve linear ODE:

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{40} sin (t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{40} sin (t)

y^{^{'''}} - y^{^{'}} = 5 cos (2 x) + 7 e^{x} + 2 x^{2}

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 36 y = e^{10 x}

y^{^{''}} - 2 y^{^{'}} + 10 y = e x cos (3 x)

5 y^{^{''}} - 2 y^{^{'}} + 80 y = 24 sin (4 t)

y^{^{''}} - 4 y = - 4

What is the solution for 4y^{''}+324y=8sin(t) ?
The solution for 4y^{''}+324y=8sin(t) is y=c_{1}cos(9t)+c_{2}sin(9t)+1/40 sin(t)