In Problems 1-21 and 24-26 use the Fourier integral transforms of this section to solve the given boundary-value problem. Make assumptions about boundedness where necessary. 9. (a) a² dx² -00 < x< ∞, t > 0 u(x, 0) = f{\x), = g(x), ∞ < x < ∞ (b) If g(x) = 0, show that the solution of part (a) can be written as u(x, f) = ; [fx+ at) + f\x- at)]. dt lt=0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Math / Bundle: Differential Equations with... / In Problems 1-21 and 24-26 use the Fourier integral transforms of this sectio...
: In Problems 1-21 and 24-26 use the Fourier integral transforms of this section to solv...
Publisher: Cengage Learning
DENNS ELA
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ISBN: 9781337604901
Chapter 14.4, Problem 9E
Textbook Problem
In Problems 1-21 and 24-26 use the Fourier integral transforms of this section to solve the given
boundary-value problem. Make assumptions about boundedness where necessary.
9.
(a) a² ³u
dx2
-00 < x< 0, t > 0
dt 2
ди
u(x, 0) = f{x),
o = g(x), ∞ < x< o∞
dt It=0
(b) If g(x) = 0, show that the solution of part (a) can be written as u(x, f) = - [fx+ at) + f{x- at)].
%3D
%3D
Expert Solution
(a)
To determine
The u (x, t) under given boundary conditions.
Answer to Problem 9E
00
G (a)
-sin aat
-jax da.
Subject to given boundary conditions u (x, t) =
(a) cos aat +
2л
Transcribed Image Text:9:06 AM Fri May 14 * 21% 0 A bartleby.com = bartleby Q Search for textbooks, step-by-step explanatio... Ask an Expert Math / Bundle: Differential Equations with... / In Problems 1-21 and 24-26 use the Fourier integral transforms of this sectio... : In Problems 1-21 and 24-26 use the Fourier integral transforms of this section to solv... Publisher: Cengage Learning DENNS ELA Find Z ISBN: 9781337604901 Chapter 14.4, Problem 9E Textbook Problem In Problems 1-21 and 24-26 use the Fourier integral transforms of this section to solve the given boundary-value problem. Make assumptions about boundedness where necessary. 9. (a) a² ³u dx2 -00 < x< 0, t > 0 dt 2 ди u(x, 0) = f{x), o = g(x), ∞ < x< o∞ dt It=0 (b) If g(x) = 0, show that the solution of part (a) can be written as u(x, f) = - [fx+ at) + f{x- at)]. %3D %3D Expert Solution (a) To determine The u (x, t) under given boundary conditions. Answer to Problem 9E 00 G (a) -sin aat -jax da. Subject to given boundary conditions u (x, t) = (a) cos aat + 2л
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