I am trying to figure out the particular ansatz (if that's all there is) for the solution to the SDE:
$ dr_t = [v_t - ar_t]dt + \sigma dW_t, $
where $a$ is constant and $v,t$ are, potentially, time-dependent. Note the difference to the standard Vasicek mean-reverting SDE.
Any help in solving this SDE is appreciated.