Use linstedts method to obtain a two-term approximation to

Question

A non-linear oscillator satisfies the equation

(1 + ∈x²)x^·· + x = 0

where ∈ is a small parameter. Use Linstedt'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 4 cos³s = 3 coss + cos 3s.]