Solving a 2nd order non-linear ODE

Question

First off, please correct me if my title is wrong.

I want to solve an equation which has the following form:

$f'' + Af^3 + Bf = 0$

The closest I have gotten to such a form was when looking as the Jacobi elliptic differential equations, but I am unsure of how to proceed. Thanks in advance.

Answer 1

Hint:

$$f'f''+(Af^3+Bf)f'=0$$

and

$$\frac12f'^2+A\frac{f^4}4+B\frac{f^2}2+C=0.$$

This is a separable equation.