Hey Tennis, I believe we can obtain an implicit solution. Some background for those not familiar with the problem: We wish to minimize the following integral over some domain D:

. Euler's necessary requirement to do this is the following:

Plugging all that in and remembering the partials treat y and y' as just regular variables but the ordinary derivative treats them as functions of x, I get (if I didn't make any errors) the following ODE:

Ok, that's a little intimidating but we can do the first integration by making the change of variable and integrating. I get:

Now integrate the inverse of at the point to obtain an implicit albeit not very satisfying expression for the solution: