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-   -   2nd order nonlinear non-seperable equation (http://www.physicsforums.com/showthread.php?t=302141)

phygeek Mar24-09 10:40 AM

2nd order nonlinear non-seperable equation
 
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 Apr4-09 02:07 AM

Re: 2nd order nonlinear non-seperable equation
 
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 Apr6-09 01:57 PM

Re: 2nd order nonlinear non-seperable equation
 
Welcome to physics forum phygeek. Why don't you try a series solution.


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