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# In this problem we outline a proof that the eigenfunctions of the Sturm-Liouville ISBN: 9781119256007 392

## Solution for problem 23 Chapter 11.2

Elementary Differential Equations and Boundary Value Problems | 11th Edition

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Problem 23

In this problem we outline a proof that the eigenfunctions of the Sturm-Liouville problem (1), (2) are real-valued. a. Let be an eigenvalue and let ( x) = U( x) + iV ( x) be a corresponding eigenfunction. 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-valued, apart from an arbitrary multiplicative constant that may be complex.

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##### ISBN: 9781119256007

The answer to “In this problem we outline a proof that the eigenfunctions of the Sturm-Liouville problem (1), (2) are real-valued. a. Let be an eigenvalue and let ( x) = U( x) + iV ( x) be a corresponding eigenfunction. 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-valued, apart from an arbitrary multiplicative constant that may be complex.” is broken down into a number of easy to follow steps, and 82 words. The full step-by-step solution to problem: 23 from chapter: 11.2 was answered by , our top Math solution expert on 03/13/18, 08:17PM. This textbook survival guide was created for the textbook: Elementary Differential Equations and Boundary Value Problems, edition: 11. Elementary Differential Equations and Boundary Value Problems was written by and is associated to the ISBN: 9781119256007. This full solution covers the following key subjects: . This expansive textbook survival guide covers 75 chapters, and 1655 solutions. Since the solution to 23 from 11.2 chapter was answered, more than 216 students have viewed the full step-by-step answer.

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