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Calulus of variations Euler Lagrange equation
Find the extremals for the following functionals and discuss whether they provide a minimum or a maximum to the functional.
$$j[y]=\int_0^1 \exp(y)(y')^2 dx $$ subject to the boundary conditions $y(0)=1$ and $y(1)=log(4)$.
I am aware that you have to find the euler lagrange equation to the problem but I am then having trouble solving it for y' and y. Also how do I know whether it provides a min or a max? I'm pretty sure I need to use this, $$ j[y+f] = \int_0^1(y'+f')^2-(y+f) dx $$ Any help would be greatly appreciated.