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.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.5: Derivatives Of Logarithmic Functions
Problem 47E
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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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