Let $$dr_t=(\alpha(t)-\beta r_t)dt+\sigma dW_t$$ where $\alpha$ is non stochastic process and $\beta$ and $\sigma$ are constant. Can we write process $r_t$ in the form $$r_t=x_t+y_t$$ where the process $x_t$ satisfies $$dx_t=-\beta x_t dt+\sigma dW_t$$ and $y_t$ be a deterministic function. I used Ito's lemma but was not useful.
Thanks in advanced.