What is the solution for x^{''}+9x=2sin(t) ?

The solution for x^{''}+9x=2sin(t) is x=c_{1}cos(3t)+c_{2}sin(3t)+1/4 sin(t)

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x^{''}+9x=2sin(t)

x^{^{''}} + 9 x = 2 sin (t)

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

Solution steps

x^{''} (t) + 9 x = 2 sin (t)

Solve linear ODE:

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

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

What is the solution for x^{''}+9x=2sin(t) ?
The solution for x^{''}+9x=2sin(t) is x=c_{1}cos(3t)+c_{2}sin(3t)+1/4 sin(t)