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Solve the follow diferential equation

  1. Feb 11, 2010 #1
    i need to solve the follow diferential equation:

    [tex](\frac{du}{dy})^2=A+Be^{2u}+C \sqrt{D+Ee^{4u}}[/tex]

    where A,B,C,D,E are nonzero.
     
  2. jcsd
  3. Feb 11, 2010 #2

    berkeman

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    Staff: Mentor

    Re: help

    What is the context of the question? Is it for schoolwork?
     
  4. Feb 11, 2010 #3
    Re: help

    not, is for my thesis. I have tried make him.
     
  5. Feb 12, 2010 #4
    Re: help

    Maple gives the following solution to your ODE (in implicit form)

    [tex] \int_k^{u(y)}\frac{d\xi}{\sqrt{A+Be^{2\xi}+C\sqrt{D+Ee^{4\xi}}}}=\pm y,[/tex]

    where k is an arbitrary constant.
     
  6. Feb 12, 2010 #5
    Re: help

    obvious, separation variables, but

    there is a way to find a explicit solution?
     
  7. Feb 16, 2010 #6
    Re: help

    Try [tex]z=e^{2\zeta}[/tex], then [tex]z=\sqrt(D/E)Sinh(\theta)[/tex]. Maple manages to integrate that, but the resulting expression is nasty
     
  8. Feb 16, 2010 #7
    Re: help

    [tex]2\zeta=ln(\sqrt(D/E)sinh(\theta))??????[/tex]
     
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