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 $x$.



Solving ODEs of the form $x'(t)=F(x(t))+f(t)$
This is not a complete answer either but at [this page](http://eqworld.ipmnet.ru/en/solutions/ode/ode-toc1.htm) you can find many special cases of your equation for which the closed form solution *is* available.


