$\displaystyle \frac{dx}{dt} = ay - bx + f(t)$

$\displaystyle \frac{dy}{dt} = cx - dy + g(t)$

$\displaystyle a,b,c,d \in \mathbb{R}$ and $\displaystyle f(t),g(t)$ are continuous functions of $\displaystyle t$

Is anyone familiar with a possible method to solve such a system (or some kind of perturbation to approx the solution)?