Consider the following mean-square differential equation: $Y^{'}_t+\alpha Y_{t} = X_{t}$ m.s. with $ Y_{0}=0$ where $X_t$ is a Gaussian random process with $\mu_{X}(t)=0$ and $R_X(\tau)=a^2\delta(\tau)$.
Find a partial differential equation for crosscorrelation function between ${Y_{t}; t\in R}$ and ${X_{t}; t\in R}$ with appropriate boundary conditions.
Is $Y_t$ wide sense stationary?
I tried squaring both sides and taking the expectation but I'm not sure that's what the question is asking for. Any help?