What is the way to solve $\displaystyle F(x)$ if:

$\displaystyle \displaystyle\frac{dF(x)}{dx}=\displaystyle\frac{G (x)-F(x)}{A}$

When $\displaystyle A$ is a contant. I think the answer should involve an integral of $\displaystyle G(x)$

Thanks,

Eran