I've recently been trying to solve the following equation:(adsbygoogle = window.adsbygoogle || []).push({});

d^{2}x/dt^{2}+ (x^{2}- a) dx/dt + (x^{2}- b)x = 0

I've reduced it to a first order equation by a simple substitution of y = dx/dt to obtain:

dy/dx = (a-x^{2}) + [(b-x^{2})x]/y = 0

However I cannot figure out how to solve this equation. Is it possible? If not can I at least find equilibrium states?

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# 2nd order nonlinear non-seperable equation

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