Find the eigenvalues 2, and eigenfunctions y,(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) x2y" + xy' + Ay = 0, y(1) = 0, y'(e) = 0 n = 1, 2, 3, . .. Y,x) = sin(na In (x)) n = 1, 2, 3, ... Need Help? Read It
Find the eigenvalues 2, and eigenfunctions y,(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) x2y" + xy' + Ay = 0, y(1) = 0, y'(e) = 0 n = 1, 2, 3, . .. Y,x) = sin(na In (x)) n = 1, 2, 3, ... Need Help? Read It
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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Find the eigenvalues 1, and eigenfunctions y (x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.)
x²y" + xy' + ly = 0, y(1) = 0, y'(e) = 0
2, = n²n?
2 2
%3D
n = 1, 2, 3, ...
Y,(x) =
sin (nt In (x) )
%3D
n = 1, 2, 3, ...
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