Is there a general (integral) solution to $du(t)= a(t)u(t)dt +\sigma(t)dz$? Is the following $u(t)=e^{-\int_{t_0}^{t} \alpha(s)ds}u(t_0)+\int_{t_0}^{t} \sigma(v)e^{-\int_v^{t}a(s)ds}dz(v)$ correct (which I have seen claimed without a justification)? z(t) is the standard Wienner process. Is there a good reference for it?