I am trying to find the extremal of
$$I[y] = \int_{-1}^{1}{y}dx$$
Subject to the constraint
$$\int_{-1}^{1}y^2+y’^2dx=1$$
And boundary conditions $y(-1)=y(1)=0$.
I used the Lagrange multiplier and Euler Lagrange equations to find that the general solution is
$$y=Ae^x+Be^{-x}+\frac{1}{2\lambda}$$
But when trying to solve for the constants I’m getting really awkward and messy values involving exponentials. Can someone point me in the right direction?