right, I think that is the same result that I get. Upon the simplification that you mentioned, and then solving the diff eq, I think it turns out to be:
Kx - x*y^-1/2 + C = 2y^1/2 : c,k are constants
and the y's cannont be combined and therefore y is a function of y.
Hopefully I am...
I am trying to find the extremal that minimizes \int_{0}^{1} \sqrt{y(1+y'^2)} dx
Because it is not explicitly a function of the free variable x, I can use the shortcut:
constant=F-y'*(dF/dy') to solve for y(x)
My problem is that after grinding through the algebra my y(x) is a function...