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Changing variables within a differential equation

Dear all,

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

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

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