Hello everybody. Sorry, I don't know how to use TeX yet, I couldn't find a testing zone. Problem: Let I = \int_0^\infty [(dy/dx)^2 - y^2 + (1/2)y^4]dx, and y(0) = 0, y(\infty) = 1. For I to be extremal, which differential equation does y satisfy? Solution: The condition is that \delta I = 0 \Rightarrow \int_0^\infty [2(dy/dx)\delta (dy/dx) -2(y-y^3)\delta y]dx = 0, which results, after partial integration, in y - y^3 + (d^2 y / dx^2) = 0, which I hope is the correct answer. The question is: why are y(0) = 0 and y(\infty) = 1, mentioned, I didn't use them at all.