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U"(x) + XU(x) = 0, 0

U"(x) + XU(x) = 0, 0

Advanced Engineering Mathematics
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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I have attached an image of the graphical method.

Question 3. Consider the eigenvalue problem U"(x)+ XU (x) = 0, 0<x< l with the mixed boundary values U'(0) – U (0) = 0, U(1) = 0. (a) Find all the eigenvalues using the graphical method (similar to textbook 4.3), discuss all cases. (b) Let An be the nth positive eigenvalue, find a simple sequence that An is asymp- totic to.
Transcribed Image Text:Question 3. Consider the eigenvalue problem U"(x)+ XU (x) = 0, 0<x< l with the mixed boundary values U'(0) – U (0) = 0, U(1) = 0. (a) Find all the eigenvalues using the graphical method (similar to textbook 4.3), discuss all cases. (b) Let An be the nth positive eigenvalue, find a simple sequence that An is asymp- totic to.
Case 2 The case of absorption at x = 0 and radiation at x = 1, but more radiation than absorption, is given by the conditions (13) аo < 0, aj > 0, аo + aj > 0. 95 4.3 THE ROBIN CONDITION 3 T/1 27/l 37/l 4 T/l
Transcribed Image Text:Case 2 The case of absorption at x = 0 and radiation at x = 1, but more radiation than absorption, is given by the conditions (13) аo < 0, aj > 0, аo + aj > 0. 95 4.3 THE ROBIN CONDITION 3 T/1 27/l 37/l 4 T/l
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