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Path: utzoo!linus!decvax!harpo!eagle!allegra!alice!apdoo
From: apdoo@alice.UUCP
Newsgroups: net.math
Subject: Re: Differential equation
Message-ID: <2335@alice.UUCP>
Date: Mon, 5-Dec-83 12:06:23 EST
Article-I.D.: alice.2335
Posted: Mon Dec  5 12:06:23 1983
Date-Received: Tue, 6-Dec-83 23:53:15 EST
References: <434@seismo.UUCP>
Organization: AT&T Bell Laboratories, Murray Hill
Lines: 22


	There is, of course, a symbolic way of solving this equation.
Writing D for the differential operator, we have
  inf   n
f=sum nD f
  n=1

so
    Df
f=---------
   (1-D)**2
Solving,
(1-D)**2 f =Df

f-3Df+D**2 f =0

f=c exp(rx) + k exp(sx)

where c and k are arbitrary constants and r and s are the roots of
1-3x+x**2=0

or (3+-sqrt(5))/2