Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Does anyone know a solution to this ODE?

  1. Jan 21, 2012 #1
    Dear all,

    I am wondering if anyone knows the solution to the following nonlinear ODE,
    \left( -3 + \frac{ f(r) f'(r)}{r} \right)(1+ f'(r)^2 ) + f(r) f''(r) = 0
    subject to the initial conditions f(R) = f(-R) = f_0.

    I have a feeling a closed form solution exists to this ODE because I know a very simple closed form solution to the related ODE
    \left( 2 + \frac{ f(r) f'(r)}{r} \right)(1+ f'(r)^2 ) + f(r) f''(r) = 0 \,.
    A solution to this ODE is
    f(r) = (R^2 - r^2)^{1/2} \,.

    Thanks in advance for any help!

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted