u(x, t)tt = u(x, t) xx to find the solution for the given initial conditions. Let h(x) be defined as follows: 0 x € (-∞, -1] x+1 x € (-1,0] h(x) = -x+1 x = (0, 1] x = (1, ∞) a. u(x,0) = h(x), ut(x,0) = 0, b. u(x,0) = 0, ut(x,0) = h(x).
u(x, t)tt = u(x, t) xx to find the solution for the given initial conditions. Let h(x) be defined as follows: 0 x € (-∞, -1] x+1 x € (-1,0] h(x) = -x+1 x = (0, 1] x = (1, ∞) a. u(x,0) = h(x), ut(x,0) = 0, b. u(x,0) = 0, ut(x,0) = h(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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Question
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Use the d'Alambert formula for the wave equation to find the solution for the given initial conditions.
![u(x, t)tt = u(x, t),
xx
to find the solution for the given initial conditions. Let h(x) be defined as follows:
0
x € (-∞, -1]
x + 1
h(x) =
x € (-1,0]
x € (0, 1]
−x+1
0
x = (1, ∞)
a. u(x,0) = h(x), ut(x, 0) = 0,
b. u(x,0) = 0, ut(x,0) = h(x).
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91f76606-a4d9-42f0-be0d-7b1366a5593f%2F95444dc3-377c-42c8-b74c-01c0c718f08b%2F2w9mowc_processed.png&w=3840&q=75)
Transcribed Image Text:u(x, t)tt = u(x, t),
xx
to find the solution for the given initial conditions. Let h(x) be defined as follows:
0
x € (-∞, -1]
x + 1
h(x) =
x € (-1,0]
x € (0, 1]
−x+1
0
x = (1, ∞)
a. u(x,0) = h(x), ut(x, 0) = 0,
b. u(x,0) = 0, ut(x,0) = h(x).
=
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