Let $B_t$ denote the standard Brownian motion process. $X_t$ and $Y_t$ are Ito diffusions with the following SDEs: \begin{align} dX_t &= \mu(t,X_t) \; dt + \sigma(t,X_t) \; dB_t \\ dY_t &= \mu(t,Y_t) \; dt + \sigma(t,Y_t) \; dB_t \end{align} What approach do I need to use to compute covariance of $X_t$ and $Y_t$? I tried to work with the associated integral equations of the above SDEs but that became too messy and did not make any sense.
I would appreciate any pointers and hints.