Find the eigenvalues and eigenfunctions for the following eigenvalue problem: X"+AX=0, A>0. X(0)=0, X'(1)=0
Find the eigenvalues and eigenfunctions for the following eigenvalue problem: X"+AX=0, A>0. X(0)=0, X'(1)=0
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 for the following eigenvalue problem:
X"+AX=0, A>0.
X(0)=0, X'(1)=0
A
A=(2n+1)/16, neZ
X = C,cos 2n+1x
4
B
A=(nT)²,
Xn=Cncos(nx), neZ
C A=(nT1)?,
Xn=Cpsin(nTx), neZ
A=(2n+1)2/4, nez
X=(2n+1)2/16, nez
X= Csin 2n+1x
4.
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