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Given the Sturm-Liouville problem. -X"(x) = AX(x), x E (0, L), X (0) - aX(0) = 0, X'(L) + bX(L) = 0, where a, b are real constants. (i) Show thatA = is an Oeigenvalue if and only if a +b = -a b L. %3D (ii) Find the eigenfunctions corresponding to the zero eigenvalue.

Given the Sturm-Liouville problem. -X"(x) = AX(x), x E (0, L), X (0) - aX(0) = 0, X'(L) + bX(L) = 0, where a, b are real constants. (i) Show thatA = is an Oeigenvalue if and only if a +b = -a b L. %3D (ii) Find the eigenfunctions corresponding to the zero eigenvalue.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve this now in 2 hours maximum and take a thumb up plz solve both parts.
Given the Sturm-Liouville problem. -X"(x) = AX(x), x E (0, L), X (0) – aX(0) = 0, X'(L) +bX(L) = 0, where a, b are real constants. (i) Show thatA = is an Oeigenvalue if and only if a +b = -a b L. %3D (ii) Find the eigenfunctions corresponding to the zero eigenvalue.
Transcribed Image Text:Given the Sturm-Liouville problem. -X"(x) = AX(x), x E (0, L), X (0) – aX(0) = 0, X'(L) +bX(L) = 0, where a, b are real constants. (i) Show thatA = is an Oeigenvalue if and only if a +b = -a b L. %3D (ii) Find the eigenfunctions corresponding to the zero eigenvalue.
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