Consider the eigenvalue problem y"+2y'+(lambda)y=0; y(0)=0, y'(1)=0. Show that the eigenvalues are all positive and that the nth positive eigenvalue is (lambda)n= an^2+1 with associated eigenfunction yn(x)= e^-x sin(anx) where anx is the nth positive root of tanz=z
Consider the eigenvalue problem y"+2y'+(lambda)y=0; y(0)=0, y'(1)=0. Show that the eigenvalues are all positive and that the nth positive eigenvalue is (lambda)n= an^2+1 with associated eigenfunction yn(x)= e^-x sin(anx) where anx is the nth positive root of tanz=z
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 66E: Show that A=[0110] has no real eigenvalues.
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Consider the eigenvalue problem y"+2y'+(lambda)y=0; y(0)=0, y'(1)=0. Show that the eigenvalues are all positive and that the nth positive eigenvalue is (lambda)n= an^2+1 with associated eigenfunction yn(x)= e^-x sin(anx) where anx is the nth positive root of tanz=z
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