Geodesic equation for the metric ds² = y²(dx² + dy²)

[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.