13. (a) Show that the following differential equation together with the bound- ary conditions is a Sturm-Liouville problem. What is the weight function? y" - 2y + xy = 0, 0≤x≤ 1, y(0) = 0, y(1) = 0. (b) Determine the eigenvalues and corresponding eigenfunctions of the problem. Fix the multiplication constant by the requirement 1 [ ₁ = Yn (x)ym (x)w(x) dx 2 0 = e Ans. (a) [e-2y'] + \e-²xy = 0, w(x) = Yn(x) = е² sin nπx. (b) An = n²π² +1, -2x -dnm.
13. (a) Show that the following differential equation together with the bound- ary conditions is a Sturm-Liouville problem. What is the weight function? y" - 2y + xy = 0, 0≤x≤ 1, y(0) = 0, y(1) = 0. (b) Determine the eigenvalues and corresponding eigenfunctions of the problem. Fix the multiplication constant by the requirement 1 [ ₁ = Yn (x)ym (x)w(x) dx 2 0 = e Ans. (a) [e-2y'] + \e-²xy = 0, w(x) = Yn(x) = е² sin nπx. (b) An = n²π² +1, -2x -dnm.
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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Plz answer both parts
![13. (a) Show that the following differential equation together with the bound-
ary conditions is a Sturm-Liouville problem. What is the weight function?
y" - 2y + xy = 0, 0≤x≤ 1,
y(0) = 0, y(1) = 0.
(b) Determine the eigenvalues and corresponding eigenfunctions of the
problem. Fix the multiplication constant by the requirement
1
[ ₁ =
Yn (x)ym (x)w(x) dx
2
0
= e
Ans. (a) [e-2y'] + \e-²xy = 0, w(x) =
Yn(x) = е² sin nπx.
(b) An = n²π² + 1,
-2x
-8nm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0694005b-3cc2-452c-9b75-517869d0a9bb%2F6c421b03-b90a-4a5f-8a25-6b1488cf16eb%2Fw2b22a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:13. (a) Show that the following differential equation together with the bound-
ary conditions is a Sturm-Liouville problem. What is the weight function?
y" - 2y + xy = 0, 0≤x≤ 1,
y(0) = 0, y(1) = 0.
(b) Determine the eigenvalues and corresponding eigenfunctions of the
problem. Fix the multiplication constant by the requirement
1
[ ₁ =
Yn (x)ym (x)w(x) dx
2
0
= e
Ans. (a) [e-2y'] + \e-²xy = 0, w(x) =
Yn(x) = е² sin nπx.
(b) An = n²π² + 1,
-2x
-8nm.
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