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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <k603ld$7lp$1@smc.vnet.net>

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?