dx de (22 dy) + λxy = 0, y(1) = 0, y′(2) = 0, form a regular Sturm-Liouville system. further that the system can be written as a constrained variational problem with functional S[y] = 2 {{² [² dx x²y'², y(1) = 0, and constraint 2 C{[y] = [{² da xy² = 1. dx Assume that the eigenvalues λ and eigenfunctions yk, k = 1, 2, . . ., exist. Working from equation (1), derive the relationship λι = 2 ♫² da ✓ dx x²y, k = 1, 2, ………. - Using the trial function z = A sin(л(x − 1)/2), show that the smallest eigenvalue, A1, satisfies the inequality (7π² - 18)π² λι Σ 6(4+32) Justify your answer briefly.