The problem is to find the fixed points for the equation:
$$\ddot{x}+ \dot{x}- x + ax^3=b \cos(ct)$$
where $a,b$ and $c$ are constants.
The Duffing oscillator is a 2nd order differential equation and I know that we can find the fixed points with the following substitution:
$$\dot{x}=y$$
Then we get a system: $$\dot{x}=y$$ $$\dot{y}=\ddot{x}$$
From the first equation we get: $$\dot{x}=y=0$$
But how do I approach the second equation? $$\dot{y}=\ddot{x}=-\dot{x}+ x - ax^3+b \cos(ct)=0$$