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?