  The goal of the present paper is to propose an enhanced ordinary differential
equations solver by exploitation of the powerful equivalence method of \'Elie
Cartan. This solver returns a target equation equivalent to the equation to be
solved and the transformation realizing the equivalence. The target ODE is a
member of a dictionary of ODE, that are regarded as well-known, or at least
well-studied. The dictionary considered in this article are ODE in a book of
Kamke. The major advantage of our solver is that the equivalence transformation
is obtained without integrating differential equations. We provide also a
theoretical contribution revealing the relationship between the change of
coordinates that maps two differential equations and their symmetry
pseudo-groups.
