Calculus of variations assignment. Kindly solve as soon as possible. Thank you

Question 3 - 22 marks (a) Show that the equation and boundary conditions dr 2-2 + Ary =0, y(1) = 0, y'(2) = 0, (1) form a regular Sturm-Liouville system. Show further that the system can be written as a constrained variational problem with functional shul = [ dizzy?, y(1) = 0. and constraint Cyl = dexy? = 1. [9] (b) Assume that the eigenvalues Ax and eigenfunctions yk, k = 1, 2, .... exist. Working from equation (1), derive the relationship Ak = dex yR, k = 1,2. .... [4] (c) Using the trial function = = Asin(#(x - 1)/2), show that the smallest eigenvalue, A1, satisfies the inequality (712 -18)12 6(4 + 372) Justify your answer briefly. [9]