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The differential operator Lis defined by d (e* 一 Ly = -e*y · - - dx dx (a) Determine the eigenvalues 1, of the problem, Ly, = \,eʻy, » 0 < x <1 dy 1 with boundary conditions y(0) = 0 +-y = 0 at x =1. dx 2 (b) Find the corresponding eigenfunctions, y,, and also a weight function p(x) with respect to which the y, are orthogonal.

The differential operator Lis defined by d (e* 一 Ly = -e*y · - - dx dx (a) Determine the eigenvalues 1, of the problem, Ly, = \,eʻy, » 0 < x <1 dy 1 with boundary conditions y(0) = 0 +-y = 0 at x =1. dx 2 (b) Find the corresponding eigenfunctions, y,, and also a weight function p(x) with respect to which the y, are orthogonal.

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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Exercise 1. The differential operator Lis defined by d dy. (e" dx 1 e*y . 4 Ly dx (a) Determine the eigenvalues A of the problem, Ly = \ e*y, , 0 < x <1 n n with boundary conditions y(0) = 0 1 dy + 0 at x =1. %3D dx 2 (b) Find the corresponding eigenfunctions, Y, , and also a weight function p(x) with respect to which the y, are orthogonal.
Transcribed Image Text:Exercise 1. The differential operator Lis defined by d dy. (e" dx 1 e*y . 4 Ly dx (a) Determine the eigenvalues A of the problem, Ly = \ e*y, , 0 < x <1 n n with boundary conditions y(0) = 0 1 dy + 0 at x =1. %3D dx 2 (b) Find the corresponding eigenfunctions, Y, , and also a weight function p(x) with respect to which the y, are orthogonal.
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