In some physical problem the following differential equation appears

$\dot{x}=F(x)+f(t)$,

where the dot denotes derivative with respect to $t$. $x$ is evidently a function of $t$. I'm wondering what the theory of differential equations knows about how to solve these kind of equation. Generic solution for arbitrarily nonlinear functions $F$ and and $f$ is desirable without making any assumptions on theses functions.

The solution can easily be found for $F(x)=x$ and for arbitrary $f(t)$. In principle, one could Taylor expand $F(x)$ in the vicinity of the origin, and do perturbation theory in terms of higher corrections, but that's quite trivial and is \textit{not} the subject of my question.

**UPD.** By making the substitution $x = u'/u$ one can reduced the above equation to a Riccati type equation provided that $F(x)$ is a quadratic polynomial in $x$.