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

If someone could help me solve this mathematica NDSolve problem, that would be really nice. Here is a related, simpler problem to the one I am having. Suppose I want to solve the nonlinear ODE

[tex]

\left(2 r + f(r) f'(r) \right) (1 + f'(r)^2) + r f(r) f''(r) = 0

[/tex]

subject to the initial conditions

[tex]

f(R) = f(-R) = 0 \,.

[/tex]

This problem is simpler than the one I actually want to solve, because in this case I know that the solution is

[tex]

f(r) = (R^2 - r^2)^{1/2} \,.

[/tex]

I would like to try and recreate the above solution by using NDSolve in mathematica. I try using the code

but I receive the error message "Power::infy: Infinite expression 1/0. encountered." I would like to recreate the solution f(r) = \sqrt{1 - r^2}.Code (Text):

NDSolve[{(2 r + f[r] f'[r]) (1 + f'[r]^2) + r f[r] f''[r] == 0,

f[1] == 0, f[-1] == 0}, f, {r, -1, 1}]

Thanks in advance for any help!

Steph

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# Mathematica: Infinite expression error when using NDSolve

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