I asked a question earlier about Calculus of Variation, but the question I gave didn't really highlight my confusion well. I've come across some other questions that I think reveal my misunderstanding. 1. The problem statement, all variables and given/known data Solve the Euler equation for the following integral: (integral from x1->x2) ∫[(y')² + √y]dx 2. Relevant equations Euler equation: ∂F/∂y - d/dx (∂F/∂y') = 0 3. The attempt at a solution F = (y')² + √y So ∂F/∂y = 1/[2√y] and d/dx (∂F/∂y') = 2y' Thus: y'' = 1/[4√y] Although it has been some time since I took an ODE course, I think that the equation above is non-trivial to solve. So either I'm mistaken and this is easy to solve or I'm going about the calculus of variations method mistakenly. With a similar problem, ∫[1+yy']²dx, I was only able to reduce it down to: y''y² + y(y')² = 0, which again I couldn't solve. I'm not looking for answers, just want to know where I'm applying the method incorrectly, or if in fact I'm missing a far easier way to apply it. Thanks for any help!