# Equilibrium and general solution of this polynomial non linear ODE

by Herr Schrödinger   Last Updated November 14, 2017 18:20 PM

I'm trying to find the equilibrium points and the general solution of this non-linear polynomial ODE, but I can't find a substitution that works....

$$\left(\frac{du}{d\phi} \right)^{2} = 2Mu^{3} - u^{2} + \frac{1}{D^{2}} \,\, ,$$

where $M,D \in \mathbb{R}$. If there is some good book in solving this, please indicate me!