My question is rather simple, and I'm sure I'm missing something simple, and yet...
I'm trying to calculate the Euler Lagrange Equations for the example function here:
http://en.wikipedia.org/wiki/First_variation
E(y(x)) = \int yy'dx
From what I can see it is:
y'-y'=0
which is clearly not very usefull. If I carry forward the first variation from (http://en.wikipedia.org/wiki/First_variation) I beleive it becomes the same thing. To me this implies that the first variation is always zero, but that can't be since some functions, $y$, clearly have more energy than others...