a) f(x) = {!- x |x| < 1 |x| > 1 ’ g(x) = 0 b) f(x) = 0 g(x) ={ sin ax |x| < 1 |x| > 1
a) f(x) = {!- x |x| < 1 |x| > 1 ’ g(x) = 0 b) f(x) = 0 g(x) ={ sin ax |x| < 1 |x| > 1
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
Pu
x E R,
t > 0,
dx2'
u(х, 0) %3D f(x),
x E R
ди
(x, 0) = g(x),
dt
x E R
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)] + IG(x + ct) – G(x – c
|
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.
a)
x2
f(x) = {
|x| < 1
I지 > 1’
g(x) =
b)
sin TX
f(x) = 0 g(x) = {"
|x| < 1
|지 > 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F143eb31c-0b16-4036-8e14-be76aa9171f0%2F71bbfe33-ac62-4f8a-a06a-f00b8b51d933%2F77kkj57_processed.png&w=3840&q=75)
Transcribed Image Text:Infinite String: consider the initial/boundary value problem
Pu
x E R,
t > 0,
dx2'
u(х, 0) %3D f(x),
x E R
ди
(x, 0) = g(x),
dt
x E R
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)] + IG(x + ct) – G(x – c
|
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.
a)
x2
f(x) = {
|x| < 1
I지 > 1’
g(x) =
b)
sin TX
f(x) = 0 g(x) = {"
|x| < 1
|지 > 1
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