In this problem we outline a proof that the eigenfunctions of the SturmLiouville problem
Chapter 11, Problem 23(choose chapter or problem)
In this problem we outline a proof that the eigenfunctions of the SturmLiouville problem (1), (2) are real. (a) Let be an eigenvalue and a corresponding eigenfunction. Let(x) = U(x) + iV(x), and show that U and V are also eigenfunctions corresponding to . (b) Using Theorem 11.2.3, or the result of 20, show that U and V are linearly dependent. (c) Show that must be real, apart from an arbitrary multiplicative constant that may be complex.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer