(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am trying to find a geodesic with Euler-Lagrange equation by varying the function

[tex] ds/d\tau = \sqrt{\dot{x} + \dot{y}} [/tex]

EDIT: it should be [tex] ds/d\tau = \sqrt{\dot{x}^2 + \dot{y}^2} [/tex]

where tau is a parametrization and the dot means a tau derivative.

However, when I plug that into the EL equation for either x or y, I get:

[tex] (\dot{x} + \dot{y})^{3/2}(\ddot{x}+\ddot{y})=0 [/tex]

How do I get a line from that?

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Variational calculus

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