2. In each case, use the d'Alambert formula for the wave equation 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 * € (-∞, -1] x+1 h(x) = x € (-1,0] x € (0, 1] -x+1 x = (1, ∞) a. u(x,0) = h(x), ut(x,0) = 0, b. u(x,0) = 0, ut(x, 0) = h(x).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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2. In each case, use the d'Alambert formula for the wave equation
u(x, t)tt = u(x, t) xx
to find the solution for the given initial conditions. Let h(x) be defined as follows:
x € (-∞, -1]
x + 1
h(x)
x € (-1,0]
x = (0, 1]
-x+1
πε(1,00)
a. u(x,0) = h(x), u₁(x,0) = 0,
b. u(x, 0) = 0, ut(x, 0) = h(x).
=
Transcribed Image Text:2. In each case, use the d'Alambert formula for the wave equation u(x, t)tt = u(x, t) xx to find the solution for the given initial conditions. Let h(x) be defined as follows: x € (-∞, -1] x + 1 h(x) x € (-1,0] x = (0, 1] -x+1 πε(1,00) a. u(x,0) = h(x), u₁(x,0) = 0, b. u(x, 0) = 0, ut(x, 0) = h(x). =
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