# Help with the Euler-Lagrange formula for a geodesic

1. Oct 20, 2009

### martinhiggs

1. The problem statement, all variables and given/known data

The metric is:

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

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

3. 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'] = 0

Now I'm stuck, please help.

2. Oct 20, 2009

### Dick

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

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