Consider the Sturm-Liouville problem
(x+1)y′′-xy′+λy=0,0<x<1,y(0)=0,y(1)=0.
(a) Based on lecture material, state some facts about the eigenvalues and corresponding eigenfunctions (without finding them!). Write a few sentences giving the reasoning for your answer.
(b) Given an arbitrary function f(x), write it as a series in the eigenfunctions, and determine an expression for the coefficients in terms of integrals. Again you don't need to find the eigenfunctions explicitly.
(c) Relate this problem to Question 2 and make some comments about the eigenvalues for this problem.
(x+1)y′′-xy′+λy=0,0<x<1,y(0)=0,y(1)=0.
(a) Based on lecture material, state some facts about the eigenvalues and corresponding eigenfunctions (without finding them!). Write a few sentences giving the reasoning for your answer.
(b) Given an arbitrary function f(x), write it as a series in the eigenfunctions, and determine an expression for the coefficients in terms of integrals. Again you don't need to find the eigenfunctions explicitly.
(c) Relate this problem to Question 2 and make some comments about the eigenvalues for this problem.
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