Consider the Euler DE x´y" + x y' + 1y = 0 for x e (1, e) with boundary conditions y'(1) = 0, y'(e) = 0 . (a) Write the DE in Sturm-Liouville form. (b) Find the positive eigenvalues 1, and corresponding eigenfunctions y„(x). (c) State the orthogonality property for these eigenfunctions, 1 ( dx - y,(x)? and also evaluate
Consider the Euler DE x´y" + x y' + 1y = 0 for x e (1, e) with boundary conditions y'(1) = 0, y'(e) = 0 . (a) Write the DE in Sturm-Liouville form. (b) Find the positive eigenvalues 1, and corresponding eigenfunctions y„(x). (c) State the orthogonality property for these eigenfunctions, 1 ( dx - y,(x)? and also evaluate
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:Consider the Euler DE x y" + x y' + 1 y = 0 for x e (1, e)
with boundary conditions y'(1) = 0, y'(e) = 0 .
(a) Write the DE in Sturm-Liouville form.
(b) Find the positive eigenvalues 1, and corresponding
eigenfunctions y,(x).
(c) State the orthogonality property for these eigenfunctions,
and also evaluate dx - y,(x)² .
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