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.

Thanks a lot in advance.

  • $\begingroup$ What is the difference between $x$ and $X$? Are the other variables constants? $\endgroup$ – Amzoti Nov 26 '13 at 13:02
  • $\begingroup$ small x is dynamical variable and capital X is constant parameter. but i edited it and replaced it by W to avoid confusion. $\endgroup$ – nitin Nov 26 '13 at 13:14

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