(a) Find the eigenvalues and eigenfunctions of the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) y"+y+Ay= 0, y(0) = 0, y(3) = 0. dx (b) Put the differential equation in self-adjoint form. [C ]]+[ y-o *** n 1, 2, 3,... (c) Give an orthogonality relation. For SC rman, ym(x)/n(x) dx = dx = 0.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 77E
Question
(a) Find the eigenvalues and eigenfunctions of the given boundary-value problem. (Give your answers in terms of n, making sure
that each value of n corresponds to a unique eigenvalue.)
y" + y + xy = 0, y(0) = 0, y(3) = 0
An=
d
dx
n = 1, 2, 3, ...
n 1, 2, 3,....
(b) Put the differential equation in self-adjoint form.
]]+([
(c) Give an orthogonality relation.
For mn,
LC
])y=0
ym(x)n(x) dx =
dx = 0.
Transcribed Image Text:(a) Find the eigenvalues and eigenfunctions of the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) y" + y + xy = 0, y(0) = 0, y(3) = 0 An= d dx n = 1, 2, 3, ... n 1, 2, 3,.... (b) Put the differential equation in self-adjoint form. ]]+([ (c) Give an orthogonality relation. For mn, LC ])y=0 ym(x)n(x) dx = dx = 0.
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