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.) y" + 2y = 0, y(-x) = 0, y(x) = 0 A2k-1 = (2k-1)2 4 Y2k-1(x) = cos(kx) 22K = K² Y(x)=sin(2kx) x k = 1, 2, 3, ... 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.) y" + 2y = 0, y(-x) = 0, y(x) = 0 A2k-1 = (2k-1)2 4 Y2k-1(x) = cos(kx) 22K = K² Y(x)=sin(2kx) x k = 1, 2, 3, ... 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 , 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.)
y" + 2y = 0, y(-x) = 0, y(x) = 0
2k-1 =
(2k-1)²
4
Y2k-1(x) = cos(kx)
22x = ²
Y2K(x) = sin(2kx)
✓
X
✓
X
k = 1, 2, 3, ...
k = 1, 2, 3, ...
k = 1, 2, 3, ...
k= 1, 2, 3, ...
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