I am a bit confused by the following problem, I am comfortable with just one Euler-Lagrange (I think!) equation but this has two and has me a bit confused :

Solve the following using Euler-Lagrange equations

Thanks for any help

(Is there any way to get LaTex anymore??)

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So this is what I have so far (didn't post earlier as I couldn't get the LaTex to work)

The Two Euler-Lagrange equations give:

1.

2.

So we may conclude that and so

substituting this into equation 2. we get

However I have no idea what to do now