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Help with 1st order ode

  1. Sep 29, 2009 #1
    does anyone have any ideas on how to solve this first order ode?

    [tex]\frac{dz}{dx} = \frac{z(x^4z^2-A^2)}{x(A^2-x^2z^4)}[/tex]

    where A is a constant.

    It's neither exact, nor homogeneous . . . nor any of the types I've been able to find for which there are techniques for solving :(

    Thank you :P
  2. jcsd
  3. Sep 30, 2009 #2
    You can find an integrating factor for your ODE to make it exact. The general solution in implicit form to your ODE is

    x^2+z^2+A^2/(xz)^2= C,

    where C is a constant.
  4. Sep 30, 2009 #3


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    Furthermore, you can solve the implicit equation for z given by kosostov by means of a clever trick.
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