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From: mkr@CS-Arthur (Mahesh K Rathi)
Newsgroups: net.math
Subject: Re: Differential equation
Message-ID: <629@CS-Arthur>
Date: Sun, 4-Dec-83 11:53:57 EST
Article-I.D.: CS-Arthu.629
Posted: Sun Dec  4 11:53:57 1983
Date-Received: Tue, 6-Dec-83 23:09:23 EST
References: <434@seismo.UUCP>
Organization: Department of Computer Science, Purdue University
Lines: 12

The solution to the infinite order differential equation

  f = f'+2f''+3f'''+ ......


  is  f(x) = exp(rx) where  r = (3-sqrt(5))/2, which is easily obtained
  by putting  f=exp(rx) in the diff. eqn.


  How did I guess that the solution should be of the type f=exp(rx) ?
  Well, by noting that the soln. to  f=f'  is exp(x), the soln. to
  f=f'+2f''  is exp(x/2) etc. etc.