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2nd Order Nonlinear ODE Question

  1. Sep 16, 2014 #1
    1. The problem statement, all variables and given/known data

    Solve the 2nd order nonlinear differential equation, with initial conditions y(0)=0 and y'(0)=1

    y''=2ay^3-(a+1)y with a within [0,1]

    It would be greatly appreciated if someone could point me in the right direction on this. Thanks!

    2. Relevant equations

    3. The attempt at a solution

    I have rearranged the equation to be y''+ya+y=2ay^3
    Last edited: Sep 16, 2014
  2. jcsd
  3. Sep 16, 2014 #2


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    Not sure how much help it is to you, but assuming ##a>0## Maple gives a solution in terms of Jacobi functions:$$
    y = \textrm{JacobiSN}(x,\sqrt a)$$
  4. Sep 16, 2014 #3
    Hmmmm, I am not sure if that helps. I will have to give that some thought...
  5. Sep 16, 2014 #4
    Any other suggestions on how to go about solving this would be helpful.
  6. Sep 17, 2014 #5


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    Use the identity [tex]y'' = y'\frac{dy'}{dy} = \frac12 \frac{d}{dy}(y'^2).[/tex]
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