Consider the equation d \\/2dy) '1 _ E( 1 xdx + ,_.____._1_x2y0, l

Consider the equation a) Decide if a Sturm-Liouville problem consisting of this equation would be regular or singular. b) Show that To(x) = 1, Tl(x) = x, and T2(x) = 2x2 -1 are eigenfunctions of such Sturm-Liouville problem, and find the corresponding eigenvalues 10, 11 , and 12. c) Using the appropriate weight function, show that Tl is orthogonal to T2 on the interval (1, 1).