The eigenvalues An and the eigenfunctions Yn of the Sturm-Liouville problem y" + 9Xy = 0, 0 < x < 2, y'(0) = 0, y(2) = 0. are O a) (2n+1)n2 , Yn (2n+1)rz An cos n> 0 2 b) An (2n+1)°r? 144, Yn = An cos , n>0 (2n +1)тх - Od dn = ", yn = An cos(), n20 COS d) (2n+1)7? (2n+1)TI , e. n > 0 Yn = Bn sin 4 e) None of these

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 65E
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The eigenvalues An and the eigenfunctions y of the Sturm-Liouville problem
y" + 9Xy = 0, 0 < x < 2, y'(0) = 0, y(2) = 0. are
a)
An
(2n+1) r?
Yn
(2n+1)T2
An cos
n > 0
4
b)
Ar
(2n+1)7?
Yn
(2n+1)r2
An cos
n> 0
144
4
Oo dn = ', Yn = An
cos (), n > 0
2
d)
(2n+1)*r?
(2n+1)T2
n> 0
, Yn = Bn sin
e) None of these
Transcribed Image Text:The eigenvalues An and the eigenfunctions y of the Sturm-Liouville problem y" + 9Xy = 0, 0 < x < 2, y'(0) = 0, y(2) = 0. are a) An (2n+1) r? Yn (2n+1)T2 An cos n > 0 4 b) Ar (2n+1)7? Yn (2n+1)r2 An cos n> 0 144 4 Oo dn = ', Yn = An cos (), n > 0 2 d) (2n+1)*r? (2n+1)T2 n> 0 , Yn = Bn sin e) None of these
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