Consider the equation(Vi-2)+ =0, -1 <*<1.d-1 < x < 1.dxdxV1 – x2a) Decide if a Sturm-Liouville problem consisting of this equation would be regular or singular.b) Show thatTo(x) = 1, T1(x) = x,and T2(x) = 2x2 – 1are eigenfunctions of such Sturm-Liouville problem, and find the corresponding eigenvalues 1o, 11, and å2.c) Using the appropriate weight function, show that T1 is orthogonal to T2 on the interval (-1, 1).

Answered: Image /qna-images/answer/bb0a8cb1-2f22-493f-84d4-a2f2389966d4.jpg

Consider the equation d 2 dy + dx -y = 0, x2 -1 < x < 1. a) Decide if a Sturm-Liouville problem consisting of this equation would be regular or singular. b) Show that To(x) = 1, T¡(x) = x, and T2(x) = 2x² – 1 are eigenfunctions of such Sturm-Liouville problem, and find the corresponding eigenvalues Ao, 11, and 12. c) Using the appropriate weight function, show that Tị is orthogonal to T2 on the interval (-1, 1).