Re: Exact solution of y' ' (x) - k*y(x)*( 1 - (y ' (x) )^4) = 0

In article <1142945580.871257.320660@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
probleman <ali.konuralp@xxxxxxxxx> wrote:

Hi;

I tried all the methods that I know and learned yet, but I could not
find it. If it is possible I want to know whether there exists an exact
solution of the equation y' ' (x) - k*y(x)*( 1 - (y ' (x) )^4) = 0 or
not.

Thanking you in advance and I'm looking forward to hearing from you
soon... Ali KONURALP


Maple gives two implicit solutions like this:


/y(x)
| / / 2 \\
| -1 + exp\2 k \z + 2 _C1//
| --------------------------------- dz = x
| (1/2)
/b / / / 2 \\\
\-1 + exp\4 k \z + 2 _C1///


where _C1 and b are arbitrary constants...
.

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