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Re: Separating functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128468] Re: Separating functions
  • From: carlos at colorado.edu
  • Date: Tue, 23 Oct 2012 00:54:57 -0400 (EDT)
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Can the following idea be exploited in some way?

If F(x,y,t)=f(x,y) g(t), then F'(x,y,t)=F(x,y) g'(t), where prime is an abbreviation for d/dt (actually
the partial derivative wrt t). Then F'/F = g'(t)/g(t) = (log(g(t)))'.  Integrating g'(t)/g(t) wrt t would
provide G(t)=log(g(t))+C, a generally complex function.  Then g(t)=exp(G) except for a 
factor exp(C).  How do I get rid of the factor?





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