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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
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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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.

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: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
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).
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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