2nd order nonlinear non-seperable equation

[phygeek]

I've recently been trying to solve the following equation:

d²x/dt² + (x² - a) dx/dt + (x² - 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-x²) + [(b-x²)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?

 

[gammamcc]

dy/dx time y comes out dy/dx times dx/dy = second derivative of x w.r.t t ?

Anyway, I see some constant solutions... Check and see. Any initial conditions on the problem?

 

[djeitnstine]

Welcome to physics forum phygeek. Why don't you try a series solution.