What is the solution for x^{''}+64x=sin(5t) ?

The solution for x^{''}+64x=sin(5t) is x=c_{1}cos(8t)+c_{2}sin(8t)+1/39 sin(5t)

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x^{''}+64x=sin(5t)

x^{^{''}} + 64 x = sin (5 t)

x = c_{1} cos (8 t) + c_{2} sin (8 t) + \frac{1}{39} sin (5 t)

Solution steps

x^{''} (t) + 64 x = sin (5 t)

Solve linear ODE:

x = c_{1} cos (8 t) + c_{2} sin (8 t) + \frac{1}{39} sin (5 t)

x = c_{1} cos (8 t) + c_{2} sin (8 t) + \frac{1}{39} sin (5 t)

0.5 y^{^{''}} + 50 y = cos (t)

x^{^{''}} + x = 1, x (0) = 2, x^{^{'}} (0) = - 1

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

\frac{d ^{2} y}{d x ^{2}} - 4 y^{^{'}} + 3 y = 8 e^{- x} + 9

(d^{2} + 9) y = cos^{4} (x)

What is the solution for x^{''}+64x=sin(5t) ?
The solution for x^{''}+64x=sin(5t) is x=c_{1}cos(8t)+c_{2}sin(8t)+1/39 sin(5t)