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