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

The solution for x^{''}+4x=sin(t) is x=c_{1}cos(2t)+c_{2}sin(2t)+1/3 sin(t)

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

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

x = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{1}{3} sin (t)

Solution steps

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

Solve linear ODE:

x = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{1}{3} sin (t)

x = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{1}{3} sin (t)

What is the solution for x^{''}+4x=sin(t) ?
The solution for x^{''}+4x=sin(t) is x=c_{1}cos(2t)+c_{2}sin(2t)+1/3 sin(t)