Dear all,(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Does anyone know a solution to this ODE?

Can you offer guidance or do you also need help?

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