All eigenvalues of a Regular Sturm-Liouville problem are strictly positive. Eigenfunctions of a Regular Sturm-Liouville System corresponding to different eigenvalues are orthogonal. The eigenvalues of a Regular Sturm-Liouville System sometimes can have two linearly independent eigenfunctions. All eigenfunctions of a regular Sturm-Liouville System are unit functions. All eigenvalues of a Regular Sturm-Liouville System are complex-valued with non- zero real part. The problem -y"(x) = xy(x), y'(0) = 1, y(1) = 2, is not a Regular Sturm-Liouville System. The problem -y"(x) + 2y'(x) + y(x) = xy(x), y(0) = 0, y(1) = 0, is a Regular Sturm-Liouville System.
All eigenvalues of a Regular Sturm-Liouville problem are strictly positive. Eigenfunctions of a Regular Sturm-Liouville System corresponding to different eigenvalues are orthogonal. The eigenvalues of a Regular Sturm-Liouville System sometimes can have two linearly independent eigenfunctions. All eigenfunctions of a regular Sturm-Liouville System are unit functions. All eigenvalues of a Regular Sturm-Liouville System are complex-valued with non- zero real part. The problem -y"(x) = xy(x), y'(0) = 1, y(1) = 2, is not a Regular Sturm-Liouville System. The problem -y"(x) + 2y'(x) + y(x) = xy(x), y(0) = 0, y(1) = 0, is a Regular Sturm-Liouville System.
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:Select all the correct statements below.
All eigenvalues of a Regular Sturm-Liouville System are real-valued.
Any continuous function defined on an closed interval can be expanded as an
infinite linear combination of eigenfunctions of a Regular Sturm-Liouville System
defined on that same closed interval.
All eigenvalues of a Regular Sturm-Liouville System are complex-valued with zero
real part.
The eigenfunctions yn (x) of a Regular Sturm-Liouville System corresponding to
an eigenvalue An, for a fixed n, are unique except for a multiplicative constant.
Transcribed Image Text:All eigenvalues of a Regular Sturm-Liouville problem are strictly positive.
Eigenfunctions of a Regular Sturm-Liouville System corresponding to different
eigenvalues are orthogonal.
The eigenvalues of a Regular Sturm-Liouville System sometimes can have two
linearly independent eigenfunctions.
All eigenfunctions of a regular Sturm-Liouville System are unit functions.
All eigenvalues of a Regular Sturm-Liouville System are complex-valued with non-
zero real part.
The problem
-y"(x) = xy(x), y'(0) = 1, y' (1) = 2,
is not a Regular Sturm-Liouville System.
The problem
-y"(x) + 2y'(x) + y(x) = xy(x), y'(0) = 0,
is a Regular Sturm-Liouville System.
y(1) = 0,
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