A differential equation is given by du ди – 3 = (i) Find the Fourier transform U(s,t) of the solution considering that at t = 0, u(x,0) = f(x). (ii) For the case where u(x, 0) = eîar, find the solution u(x,t).
A differential equation is given by du ди – 3 = (i) Find the Fourier transform U(s,t) of the solution considering that at t = 0, u(x,0) = f(x). (ii) For the case where u(x, 0) = eîar, find the solution u(x,t).
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
A differential equation is given by:
(delta)2u/(delta)x2 - 3(delta)u/(delta)x = (delta)u/(delta)t
i) Find the Fourier transform U(s,t) of the solution considering that at t = 0 u(x,0) = f(x).
ii) For the case where u(x,0) = eiax, find the solution u(x,t).
A better formatted version of this question is attached, as well as the Fourier transform definition to be used.
Transcribed Image Text:The Fourier transform:
(Ff)(s) = f(s) = F(s) = | f (t)e¬2ñist
dt
evaluated @s
defined on the frequency (s) domain
The inverse Fourier transform:
(F-'g) (t) = ğ(t) = g(t) = | g(s)e2rist ds
2πist
evaluated @t
Transcribed Image Text:A differential equation is given by
ди
- 3
Ət
(i) Find the Fourier transform U(s,t) of the solution considering that at t = 0,
u(x,0) = f(x).
(ii) For the case where u(x, 0) = eiar, find the solution u(x, t).
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