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Help with a difficult ODE

  1. Jan 25, 2010 #1
    This is really difficult for me(at least for me), though it seems simple!
    Could anyone help me to solve it or give some suggestion?


    Thank you!
  2. jcsd
  3. Jan 26, 2010 #2


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    Welcome to PF!

    Hi hyime! Welcome to PF! :smile:

    (try using the X2 tag just above the Reply box :wink:)

    Hint: if D represents "differentiate", then this is (D2 + C1D + C2)y = 0 :smile:
  4. Jan 26, 2010 #3


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    Re: Welcome to PF!

    No, it isn't. The second term has [itex]y^2[/itex], not y'. That's a non-linear d.e. and is NOT simple.
  5. Jan 26, 2010 #4


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    oops! :biggrin:

    show how it pays to write clearly! :smile:
  6. Jan 26, 2010 #5
    The integrating factor to your ODE is y', so


    is an exact ODE, that is it can be presented as




    where c is an arbitrary constant. The last first order ODE (with constant coefficients) is solvable by "separation of variables".
  7. Jan 26, 2010 #6
    Look for elliptic functions and it's associated differential equation.
  8. Jan 26, 2010 #7
    Thank you for all your help, I am working on it.
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