Originally Posted by

**Showcase_22** I'm finding this odd since the only functions i've looked at are of the form $\displaystyle g(x,y,y')$ not $\displaystyle f(y',y'',y''')$.

I only thought the Euler-Lagrange equations were defined the the first type of function, not the second.

Would I do it like this:

$\displaystyle \frac{\partial f}{\partial y'''}=y'$

$\displaystyle \frac{\partial f}{\partial y''}=2(y'')$

So the E-L equation is $\displaystyle 2(y'')-\frac{d}{dy'}(y')=0$

Which becomes $\displaystyle 2y''-1=0$