What is the solution for x^{''}+4x=32sin(4t) ?

The solution for x^{''}+4x=32sin(4t) is x=c_{1}cos(2t)+c_{2}sin(2t)-8/3 sin(4t)

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x^{''}+4x=32sin(4t)

x^{^{''}} + 4 x = 32 sin (4 t)

x = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{8}{3} sin (4 t)

Solution steps

x^{''} (t) + 4 x = 32 sin (4 t)

Solve linear ODE:

x = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{8}{3} sin (4 t)

x = c_{1} cos (2 t) + c_{2} sin (2 t) - \frac{8}{3} sin (4 t)

What is the solution for x^{''}+4x=32sin(4t) ?
The solution for x^{''}+4x=32sin(4t) is x=c_{1}cos(2t)+c_{2}sin(2t)-8/3 sin(4t)