Consider the functional S[y] = ay(1)² + [* dx ßy², y(0) = 0, with a natural boundary condition at x = 1 and subject to the constraint C[y] = √y(1)² + [* dx w(x) y² = 1 1, where a, ẞ and y are nonzero constants. Euler-Lagrange equation β d²y В 1х2 dx² +\w(x)y=0, y(0) = 0, (a− yλ) y(1) + ßy' (1) = 0, where is a Lagrange multiplier. = Let w(x) = 1 and a = B = y = 1. Find the nontrivial stationary paths, stating clearly the eigenfunctions y (normalised so that C[y] = 1) and the values of the associated Lagrange multiplier.