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Dear All,

I have following first order nonlinear ordinary differential and i was wondering if you can suggest some method by which either i can get an exact solution or approaximate and converging perturbative solution.

[tex]\frac{dx}{dt} = 2Wx + 2xy - 4x^{3}[/tex][tex]\frac{dy}{dt} = \gamma \, (x^{2} - y)[/tex]

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.

Also If somebody can help me about how I can use fixed point analytic method to solve this differential equations and some references on it, will be very useful too.

Thanks a lot in advance.

PS. I tried homotopy perturbation analysis and simple iteration procedure to try to solve it and it diverges after some time(good only for early short times).

I have following first order nonlinear ordinary differential and i was wondering if you can suggest some method by which either i can get an exact solution or approaximate and converging perturbative solution.

[tex]\frac{dx}{dt} = 2Wx + 2xy - 4x^{3}[/tex][tex]\frac{dy}{dt} = \gamma \, (x^{2} - y)[/tex]

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.

Also If somebody can help me about how I can use fixed point analytic method to solve this differential equations and some references on it, will be very useful too.

Thanks a lot in advance.

PS. I tried homotopy perturbation analysis and simple iteration procedure to try to solve it and it diverges after some time(good only for early short times).

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