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Which of the following gives the eigenvalues and eigenfunctions of the Sturm-Liouville problem (SLP) y"(x) + Ay(x) = 0, y'(0) = 0, y(2) = 0. (Hint: There is no eigenvalue for 1< 0) A An = [ , (2п-1) π Yn (x) = Cn cos 8 (2n-1) -пх|,Сп + 0, п %3D 1,2, ... An = (nn)², yn (x) = cn cos(nnx),cn # 0, n = 1,2, .... %3D (2n-1) An = [], y,(x) = c, sin [nx].Cn + 0, n = 1,2, . (2n-1) D An 3 (), УлСх) — сп sin (x), сп + 0, п %3D 1,2, ... y,(x) = cn cos (2n-1) (2n-1) пх|,сп + 0, п %3D 1,2, ....

Which of the following gives the eigenvalues and eigenfunctions of the Sturm-Liouville problem (SLP) y"(x) + Ay(x) = 0, y'(0) = 0, y(2) = 0. (Hint: There is no eigenvalue for 1< 0) A An = [ , (2п-1) π Yn (x) = Cn cos 8 (2n-1) -пх|,Сп + 0, п %3D 1,2, ... An = (nn)², yn (x) = cn cos(nnx),cn # 0, n = 1,2, .... %3D (2n-1) An = [], y,(x) = c, sin [nx].Cn + 0, n = 1,2, . (2n-1) D An 3 (), УлСх) — сп sin (x), сп + 0, п %3D 1,2, ... y,(x) = cn cos (2n-1) (2n-1) пх|,сп + 0, п %3D 1,2, ....

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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Which of the following gives the eigenvalues and eigenfunctions of the Sturm-Liouville problem (SLP) y"(x) + ly(x) = 0, y'(0) = 0, y(2) = 0. (Hint: There is no eigenvalue for 1 < 0) A (2п-1) (2п-1) An = [ , y,(x) = cn cos [ x|, Cn + 0, n = 1,2, .. 8 B An 3 (пл)?, уn (x) — с, cos(ппх), с, + 0, п — 1,2, .... (2n-1) (2п-1) = C, sin [nx], Сп + 0, п %3 1,2, .... 2 D 2 (), Yn(x) = cn sin (x),Cn + 0, n = 1,2, ... E a, y,x) = Cn cos (2n-1) πχ [(2n-1) Tx, Cn + 0, n = 1,2, .... 4 4
Transcribed Image Text:Which of the following gives the eigenvalues and eigenfunctions of the Sturm-Liouville problem (SLP) y"(x) + ly(x) = 0, y'(0) = 0, y(2) = 0. (Hint: There is no eigenvalue for 1 < 0) A (2п-1) (2п-1) An = [ , y,(x) = cn cos [ x|, Cn + 0, n = 1,2, .. 8 B An 3 (пл)?, уn (x) — с, cos(ппх), с, + 0, п — 1,2, .... (2n-1) (2п-1) = C, sin [nx], Сп + 0, п %3 1,2, .... 2 D 2 (), Yn(x) = cn sin (x),Cn + 0, n = 1,2, ... E a, y,x) = Cn cos (2n-1) πχ [(2n-1) Tx, Cn + 0, n = 1,2, .... 4 4
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