We have the following equation:
$$mx'' + cx' +k(x^3-x)=0$$
By choosing m,c,k properly, we may simplify it to have the following system:
$$x' = y,\qquad y' = x - x^3 - ay$$
a) Find fixed points of the system
b) Characterize the fixed points' stability by linearization.
I have no idea how to find fixed points (i.e, equilibrium points) of this problem. Any help?