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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 5 y^{^{'}} + 4 y = - 2 e^{3 t}

y^{^{''}} + 4 y = 8 e^{2 t}

y^{^{''}} - 4 y^{^{'}} + 3 y = e^{(3 x)}

y^{^{''}} + 3 y^{^{'}} - 4 y = 7 e^{x}

y^{^{''}} + 25 y = 2 x, y (0) = 1, y^{^{'}} (0) = 5

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