How can I find the y(x) that minimizes the functional J?

[muzialis]

Hello there,

I am dealing with the functional (http://en.wikipedia.org/wiki/First_variation)

J = integral of (y . dy/dx) dx

When trying to compute the Euler Lagrange eqaution I notice this reduces to a tautology, i.e.

dy/dx - dy/dx = 0

How could I proceed for finding the y(x) that effectively minimizes the functional?

Thank you very much

Yours

Muzialis

 

[dextercioby]

It might help to observe that the integral can be performed directly and the functional dependence is lost.