Help with the Euler-Lagrange formula for a geodesic

[martinhiggs]

Homework Statement

The metric is:

ds^{2} = y^{2}(dx^{2} + dy^{2})

I have to find the equation relating x and y along a geodesic.

The Attempt at a Solution

ds = \sqrt{ydx^{2} + ydy^{2}} - is this right?

ds = \sqrt{y + yy'^{2}} dx

F = \sqrt{y + yy'^{2}}

So then I apply the Euler-Lagrange equation

dF/dy - d/dx[dF/dy'] = 0Now I'm stuck, please help.

 

[Dick]

It's a y^2 inside the square root, isn't it? Not a y.