- #1

insynC

- 68

- 0

## Homework Statement

Solve the Euler equation for the following integral:

(integral from x1->x2) ∫[(y')² + √y]dx

## Homework Equations

Euler equation:

∂F/∂y - d/dx (∂F/∂y') = 0

## 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!