How Do You Solve a Nonlinear Differential Equation with Polynomial Terms?

[coverband]

Homework Statement

$$\frac{d^2x}{dt^2}-x-ax^2+bx^3=0$$

Homework Equations

Please help me start this. I've never seen a d.e. with $$ax^2+bx^3$$

The Attempt at a Solution

I think it ends as a fourier. Not sure. Please help me start!

 

[madmike159]

Are you given any other values?