Find the eigenvalues A, and eigenfunctions y,(x) for the given boundary-value problem. (Give your answers in terms of k, making sure that each value of k corresponds to two unique eigenvalues.) у"+ Лу 0, у(-п) - 0, у(п) - 0 dzk -1 = k = 1, 2, 3, ... 2k - 1(x) = k = 1, 2, 3, ... k = 1, 2, 3, ... k = 1, 2, 3, ...
Find the eigenvalues A, and eigenfunctions y,(x) for the given boundary-value problem. (Give your answers in terms of k, making sure that each value of k corresponds to two unique eigenvalues.) у"+ Лу 0, у(-п) - 0, у(п) - 0 dzk -1 = k = 1, 2, 3, ... 2k - 1(x) = k = 1, 2, 3, ... k = 1, 2, 3, ... k = 1, 2, 3, ...
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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Transcribed Image Text:Find the eigenvalues 1, and eigenfunctions y,(x) for the given boundary-value problem. (Give your answers in terms of k, making sure that each value of k corresponds to two unique eigenvalues.)
у" + Лу %3D 0, у(-п) %3D 0, у(п) %3D о
12k - 1
k = 1, 2, 3, ...
Y2k – 1(x) = |
k = 1, 2, 3, ...
k = 1, 2, 3, ...
Y2k(x) =
k = 1, 2, 3, ...
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