I have following first order nonlinear ordinary differential and i was wondering if someone can suggest some method by which either i can get an exact solution or approximate and converging perturbative solution.
$$ \frac{dx}{dt} = 4(1-W^{-1}) x + \frac{4xy}{W} - 8x^{2}\\ \frac{dy}{dt} = \gamma W (x - \frac{y}{W}) $$
I want to solve it for small initial conditions i.e. close to zero for an important behavior.
Kindly help me with any methods you that might work and it will be great if you can provide few references where i can read about those methods.