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

The solution for x^{''}-x=sin(t) is x=c_{1}e^t+c_{2}e^{-t}-1/2 sin(t)

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x^{''}-x=sin(t)

x^{^{''}} - x = sin (t)

x = c_{1} e^{t} + c_{2} e^{- t} - \frac{1}{2} sin (t)

Solution steps

x^{''} (t) - x = sin (t)

Solve linear ODE:

x = c_{1} e^{t} + c_{2} e^{- t} - \frac{1}{2} sin (t)

x = c_{1} e^{t} + c_{2} e^{- t} - \frac{1}{2} sin (t)

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