The differential equation:
$$\ddot{x}(t)+\sin(\omega t)x(t)=cos(\eta t)$$ has an analytical solution involving Mathieu functions. This is valid if both $\omega$ and $\eta$ are constant. Suppose the term $\eta$ is a normal distribuited random variable $\eta(t)$ with mean $\mu$ equal to zero and variance $\sigma^2$. How changes the solution? Or better: Is it possible to find analytically the spectrum of $x(t)$? Thanks