Nonlinear frequency shift

Question

I came across the following equation: $\frac{dz}{dt}+iz=iεxy^{2}$, t is a dimensionless time, $z=x+\frac{idx}{dt}$, $y=\frac{dx}{dt}$. I would like to find a nonlinear frequency shift. I tried to decompose the right part by composing only resonant terms, but I did not come to success.