(a) Consider the following eigenvalue problem: X" + XX = 0 X'(0) = 0, X(T) = 0. (i) Show that all the eigenvalues satisfy >> 0. (ii) Find all eigenvalues and eigenfunctions. (b) Solve the following wave equation with mixed boundary conditions on an interval. (You can make use of the results obtained in (a).) Utt- c²Uax = 0 U₂(0, t) = 0, U(π, t) = 0 U (x,0) = 0, Ut(x, 0) = 6c · cos(x). .
(a) Consider the following eigenvalue problem: X" + XX = 0 X'(0) = 0, X(T) = 0. (i) Show that all the eigenvalues satisfy >> 0. (ii) Find all eigenvalues and eigenfunctions. (b) Solve the following wave equation with mixed boundary conditions on an interval. (You can make use of the results obtained in (a).) Utt- c²Uax = 0 U₂(0, t) = 0, U(π, t) = 0 U (x,0) = 0, Ut(x, 0) = 6c · cos(x). .
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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part b please
Transcribed Image Text:(a) Consider the following eigenvalue problem:
X" + XX = 0
X'(0) = 0, X(T) = 0.
(i) Show that all the eigenvalues satisfy >> 0.
(ii) Find all eigenvalues and eigenfunctions.
(b) Solve the following wave equation with mixed boundary conditions on an interval.
(You can make use of the results obtained in (a).)
Utt- c²Uxx = 0
U₂(0, t) = 0, U(π, t) = 0
U (x,0) = 0, Ut(x, 0) = 6c · cos(x).
.
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