# [Maxima] my mistake: subst(a,f(x)*g(x),eq)

N.A.Beishuizen at ctw.utwente.nl N.A.Beishuizen at ctw.utwente.nl
Thu Oct 30 15:42:26 CDT 2008

```Again, I should be more careful with my examples ;-)

ratsubst suffices for my purposes, thank you for pointing this function out.

In symmetry analysis, you consider the prolongation of the group of transformations
G acting on the variables x,y,y',... admitted by the differential equation F(x,y,y').
in the more serious case of pde's, the separation of variables rule
(which is actually a result from symmetry analysis) predicts that a lot of solutions
of linear pde's can be written as u(x,y)=f(x)*g(y) ( +f2(x)*g2(y) etc...)
In the prolonged space (x,u,du/dx,du/dy,..), occurences of f(x)*g(y) are therefore
independent on x and can be replaced simply by 'u'.

Well, not the most useful mathematical exercise in the world, but it taught me a great deal
about how (not) to do things in maxima. I can now get the determining equations for
nonlinear second order ode's. W00t!

Regards,
Nijso

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