Answered: Consider the eigenvalue problem X" (x)…

Consider the eigenvalue problem X" (x) -pX(x) = 0 (0 < x < 1) X'(0) = -X(0), X'(1) = -X(1), where p is a constant. Is p = 0 an eigenvalue? Show the reason by a mathematical argument.

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.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 12CR

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Question

Consider the eigenvalue problem
X"(x) - pX(x) = 0
(0 < x < 1)
1
X'(0) = −X(0), _X'(1) = −X(1),
where p is a constant.
Is p = 0 an eigenvalue? Show the reason by a mathematical argument.

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