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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,
    [tex]
    \left( -3 + \frac{ f(r) f'(r)}{r} \right)(1+ f'(r)^2 ) + f(r) f''(r) = 0
    [/tex]
    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
    [tex]
    \left( 2 + \frac{ f(r) f'(r)}{r} \right)(1+ f'(r)^2 ) + f(r) f''(r) = 0 \,.
    [/tex]
    A solution to this ODE is
    [tex]
    f(r) = (R^2 - r^2)^{1/2} \,.
    [/tex]

    Thanks in advance for any help!

    Steph
     
  2. jcsd
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