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