(a) Write down the general solutions for the wave equation Utt - Uxx = 0. (b) Solve the following Goursat problem Utt-Uxx = 0, x = R Ux-t=0 = 4x2 Ux+t=0 = 0 (c) Describe the domain of influence and domain of dependence for wave equations. (d) Solve the following inhomogeneous wave equation with initial data. Utt - Uxx = 2, x ЄR U(x, 0) = 0 Ut(x, 0) = COS X
(a) Write down the general solutions for the wave equation Utt - Uxx = 0. (b) Solve the following Goursat problem Utt-Uxx = 0, x = R Ux-t=0 = 4x2 Ux+t=0 = 0 (c) Describe the domain of influence and domain of dependence for wave equations. (d) Solve the following inhomogeneous wave equation with initial data. Utt - Uxx = 2, x ЄR U(x, 0) = 0 Ut(x, 0) = COS X
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 27E
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
Transcribed Image Text:(a) Write down the general solutions for the wave equation Utt - Uxx = 0.
(b) Solve the following Goursat problem
Utt-Uxx = 0, x = R
Ux-t=0
=
4x2
Ux+t=0 =
0
(c) Describe the domain of influence and domain of dependence for wave equations.
(d) Solve the following inhomogeneous wave equation with initial data.
Utt - Uxx = 2, x ЄR
U(x, 0) = 0
Ut(x, 0)
= COS X
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