Find the eigenvalues and eigenfunctions for the differential operator L(y)=-y" with boundary conditions y' (0) = 0 and y(3) = 0, which is equivalent to the following BVP y" + Ay = 0, y' (0) = 0, y(3) = 0. (a) Find all eigenvalues ,, as function of a positive integer n 1. Σ (b) Find the eigenfunctions y, corresponding to the eigenvalues A,, found in part (a). Yn (x) = Σ

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Find the eigenvalues and eigenfunctions for the differential operator L(y) = -y" with boundary conditions y' (0) = 0 and y(3) = 0, which is equivalent to the following BVP
y" + xy = 0,
y' (0) = 0, y(3) = 0.
(a) Find all eigenvalues ,, as function of a positive integer n > 1.
An =
Σ
(b) Find the eigenfunctions yn corresponding to the eigenvalues A₁, found in part (a).
Yn (x) =
Σ
Transcribed Image Text:Find the eigenvalues and eigenfunctions for the differential operator L(y) = -y" with boundary conditions y' (0) = 0 and y(3) = 0, which is equivalent to the following BVP y" + xy = 0, y' (0) = 0, y(3) = 0. (a) Find all eigenvalues ,, as function of a positive integer n > 1. An = Σ (b) Find the eigenfunctions yn corresponding to the eigenvalues A₁, found in part (a). Yn (x) = Σ
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