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3rd order nonlinear ODE

  1. Apr 21, 2004 #1
    Hi, everybody.
    I have an ODE:
    I know that it has an analytic solution, but I cannot get it (yet).
    Can anybody help me?
    (I don't need a full explanation how to solve it, just some hints or just the solution with 3 arbitrary constants).
    Thanks beforehand,
  2. jcsd
  3. Aug 25, 2009 #2


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    Three constants? That would be the case if the ODE was linear.

    There is another problem here. The ODE is autonomous, and all functions of the form y=const. are solutions, plus the solutions cannot meet each other. So this ODE has only trivial solutions.
  4. Aug 25, 2009 #3
    How about:
    [tex]y = \frac{6}{x+a}[/tex]
  5. Aug 25, 2009 #4


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    How about ...you re right?
    I mistakingly assumed that every solution has to meet the y axis.
  6. Sep 10, 2009 #5
    You are right, this ODE has an analytic general solution, but it is not so simple and includes hypergeom functions and so on. To see the solution in implicit form use Maple with


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