I have been trying to solve the following ODE
\begin{equation*} \dfrac{d\pi}{dx}x=c_1+\pi(x) c_2 + \pi(x)^2(c_3-x), \end{equation*} where, for every $i=1,2,3$, $c_i$ is a constant real value.
Separation of variables does not seem to work here, because of the term $\pi^2(x)(c_3-x)$. This equation looks like a Ricatti Equation for which a particular coordinate change could lead to a linear ODE. Does someone knows how to find it?
Best,