sin nx |x| < 1 |지 > 1 f(x) = 0 g(x) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Infinite String: consider the initial/boundary value problem
хER,
t > 0,
dx2'
u(х, 0) %3D F(x),
x E R
ди
(x, 0) = g(x),
x E R
dt
where f and g are two given twice differentiable functions. We showed in class that this problem is solved by
he d'Alembert's solution
1
u(x, t) = [f(x + ct) + f(x – ct)] +
[G(x + ct) – G(x – ct)],
2c
where G is an antiderivative of g. Sketch the solution for t = 0, 1, 2, 3, where f(x) and g(x) are given below.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90b42026-ffd5-4641-b1f2-8aa8b085cbc7%2F6d262692-a122-4fc4-a9cb-c5e692279c20%2F0jhfdzu_processed.png&w=3840&q=75)
Transcribed Image Text:Infinite String: consider the initial/boundary value problem
хER,
t > 0,
dx2'
u(х, 0) %3D F(x),
x E R
ди
(x, 0) = g(x),
x E R
dt
where f and g are two given twice differentiable functions. We showed in class that this problem is solved by
he d'Alembert's solution
1
u(x, t) = [f(x + ct) + f(x – ct)] +
[G(x + ct) – G(x – ct)],
2c
where G is an antiderivative of g. Sketch the solution for t = 0, 1, 2, 3, where f(x) and g(x) are given below.
Transcribed Image Text:b)
{
|x| < 1
|x| > 1
sin TX
f(x) = 0 g(x) =
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