# Does exact solution for these nonlinear ODE's exist?

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 approaximate and converging perturbative solution.

\begin{align*} \dfrac{dx}{dt} &= 2(1-W^{-1}) x + \dfrac{2xy}{W} - 8x^{2}\\ \dfrac{dy}{dt} &= \gamma W (x - \dfrac{y}{W}) \end{align*}

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.

Any help will be highly helpful.

• What is the difference between $x$ and $X$? Are the other variables constants? – Amzoti Nov 26 '13 at 13:02