Find the eigenvalues , 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' + Ày = 0, y'(e¯') = 0, y(1) = 0 n = 1, 2, 3, ... Y,(x) = n = 1, 2, 3, ...
Find the eigenvalues , 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' + Ày = 0, y'(e¯') = 0, y(1) = 0 n = 1, 2, 3, ... Y,(x) = n = 1, 2, 3, ...
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 \(\lambda_n\) and eigenfunctions \(y_n(x)\) 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.)
\[x^2 y'' + xy' + \lambda y = 0, \quad y(e^{-1}) = 0, \quad y(1) = 0\]
\[
\lambda_n = \underline{\hspace{3cm}} \quad n = 1, 2, 3, \ldots
\]
\[
y_n(x) = \underline{\hspace{3cm}} \quad n = 1, 2, 3, \ldots
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c39d812-58a1-4630-9d2c-3fab5b52adb8%2F8cdb6c41-38b4-49d0-9ae4-b7e791c51458%2Fvn16ox6_processed.png&w=3840&q=75)
Transcribed Image Text:Find the eigenvalues \(\lambda_n\) and eigenfunctions \(y_n(x)\) 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.)
\[x^2 y'' + xy' + \lambda y = 0, \quad y(e^{-1}) = 0, \quad y(1) = 0\]
\[
\lambda_n = \underline{\hspace{3cm}} \quad n = 1, 2, 3, \ldots
\]
\[
y_n(x) = \underline{\hspace{3cm}} \quad n = 1, 2, 3, \ldots
\]
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