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(tricky) first order ODE

  1. Apr 15, 2006 #1
    Does anyone see how one can tackle the following ODE?

    [tex] [2y*exp^{y/x} + x}] \frac {dy} {dx} -2x - 2y = 0 [/tex]

    that is my attempt:

    rearrange to get

    [tex] dy/dx = \frac {2x + 2y} {2y*exp^{y/x}-x} [/tex]

    I do not see how to go on from here. Surely, the ODE is not seperabale and I don't find a way to get the integrating factor here.

    thanks for any hints!

    [edit:] for a more clearly written version of the ODE see attached file

    Attached Files:

    Last edited: Apr 15, 2006
  2. jcsd
  3. Apr 15, 2006 #2


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    Staff Emeritus
    Science Advisor

    First thought would be to try a change of variable, u = y/x, so

    du/dx = (1/x) dy/dx - y/x2 = (1/x) dy/dx - u/x
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