dxd (2² dy) ++ λxy = 0, y(1) = 0, y′(2) = 0,form a regular Sturm-Liouville system.Show further that the system can be written as a constrainedvariational problem with functionalS[y] = [² dx x²y², y(1) = 0,and constraintC[v] = [{²*drzy² = 1.dx

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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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dx d (2² dy) + + λxy = 0, y(1) = 0, y′(2) = 0, form a regular Sturm-Liouville system. Show further that the system can be written as a constrained variational problem with functional S[y] = [² dx x²y², y(1) = 0, and constraint C[v] = [{²*drzy² = 1. dx