Given that the eigenvalues and eigenfunctions of the SLP y"+Ay = 0, y(0) = 0, y(L) = 0 %3D An = ) and y, = sin (), are nE N L. Let the BVP ut = 2ux, 0< x <÷, t>0 u(0,t) = u (; t) = 0 u(x,0) = sin(9nx) u,(x, 0) = 0 Then the solution of the BVP is

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
Author:Ron Larson
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Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 66E: Show that A=[0110] has no real eigenvalues.
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Given that the eigenvalues and eigenfunctions of the SLP
y"+Ay = 0,
y(0) = 0,
y(L) = 0
are
and y, = sin
nE N
Let the BVP ut = 2ux, 0< x <;, t> 0
u(0, t) = u (;, t) = 0
H«G.+) = 0
%
u(x,0) = sin(9nx)
u,(x, 0) = 0
hen the solution of the BVP is
Transcribed Image Text:Given that the eigenvalues and eigenfunctions of the SLP y"+Ay = 0, y(0) = 0, y(L) = 0 are and y, = sin nE N Let the BVP ut = 2ux, 0< x <;, t> 0 u(0, t) = u (;, t) = 0 H«G.+) = 0 % u(x,0) = sin(9nx) u,(x, 0) = 0 hen the solution of the BVP is
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