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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?

    y''+C1*y^2+C2*y=0

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

    tiny-tim

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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

    HallsofIvy

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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

    tiny-tim

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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

    y'(y''+C1*y^2+C2*y)=0

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

    (2/3*C1*y^3+C2*y^2+(y')^2)'=0

    or

    2/3*C1*y^3+C2*y^2+(y')^2=c

    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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