1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    pasmith

    User Avatar
    Homework Helper

    Use the identity [tex]y'' = y'\frac{dy'}{dy} = \frac12 \frac{d}{dy}(y'^2).[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: 2nd Order Nonlinear ODE Question
Loading...