Euler-Lagrange Equation for a Stationary Action

[WannabeNewton]

Homework Statement

If L(y, y', x) = y$$^{2}$$ + y'$$^{2}$$ then find the appropriate Euler Lagrange Equation. I have absolutely no idea how to solve this. I used the differential form of the Euler Lagrange equations for a stationary action but the answer i got was nothing like the answer in the book so could anyone show me how to find the equation using the differential form?

 

[Dick]

This is perfectly straightforward. Can you show us what you got and what the books answer is?

 

[WannabeNewton]

This is perfectly straightforward. Can you show us what you got and what the books answer is?

Never mind I got it I keep forgetting the dynamical variables are actually functions and I keep treating them like variables in the equation. Stupid mistakes on my part. Sorry.