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2nd order nonlinear non-seperable equation

  1. Mar 24, 2009 #1
    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?
  2. jcsd
  3. Apr 4, 2009 #2
    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?
  4. Apr 6, 2009 #3


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    Gold Member

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