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Changing variables within a differential equation

• To: mathgroup at smc.vnet.net
• Subject: [mg105012] Changing variables within a differential equation
• From: riccardo benini <riccardo.benini at gmail.com>
• Date: Tue, 17 Nov 2009 05:17:41 -0500 (EST)

Dear all,

I've been looking for a while on the web for the solution of the following
problem:

given a (partial) differential equation F(y''[x], y'[x], y[x], x)==0  (where
y and x may be though as multidimensional),
how can I correctly set up a change of variables y -> y[g],  x -> x[t],
and get an equation in g[t]:   F2(g''[t], g'[t], g[t], t)==0?


I think that this is an old problem for the Mathematica community (and
probably settled down),
but I can't figure out how to solve it and write a procedure able to do it.

Thanks in advance,
Riccardo Benini