I am looking for the general solutions of this equation in [tex]z(r)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

If someone remembers well, this equation arises in surface tension physics.

[tex]z(r)=\frac{1}{r}\frac{d}{dr}\left[\frac{z_r r}{(1+z_r^2)^{1/2}}\right][/tex]

subject to the boundary conditions

[tex]z_r(0)=z_{ro}[/tex] and

[tex]z(\infty)=0[/tex]

I only come up with rough approximations expanding the RHS around r=0, but I don't realise how might a closed solution be obtained.

Any hints?

Thanx.

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# Brave ODE

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