A non-linear oscillator satisfies the equation
(1+ϵx2)x¨+x=0,
where ϵ is a small parameter. Use Lindstedt's method to obtain a two-term approximation to the oscillation frequency when the oscillation has unit amplitude. Find also the corresponding two-term approximation to x(t). [You will need the identity 4cos3s=3coss+cos3s.]