How can I find an extremal for the following functional: $$J[y] = \int_0^1 e^y (y')^2 dx $$
with the boundary conditions $y(0)=1, y(1)=\log(4)$? I have tried computing the Euler-Lagrange equation but it becomes overly complicated.
How can I find an extremal for the following functional: $$J[y] = \int_0^1 e^y (y')^2 dx $$
with the boundary conditions $y(0)=1, y(1)=\log(4)$? I have tried computing the Euler-Lagrange equation but it becomes overly complicated.