  The aim of the paper is to demonstrate the superiority of Cartan's method
over direct methods based on differential elimination for handling otherwise
intractable equivalence problems. In this sens, using our implementation of
Cartan's method, we establish two new equivalence results. Weestablish when a
system of second order ODE's is equivalent to flat system (second derivations
are zero), and when a system of holomorphic PDE's with two independent
variables and one dependent variables is flat. We consider the problem of
finding transformation that brings a given equation to the target one. We shall
see that this problem becomes algebraic when the symmetry pseudogroup of the
target equation is zerodimensional. We avoid the swelling of the expressions,
by using non-commutative derivations adapted to the problem.
