  In all the practical applications of partial differential equations, what is
mostly needed and what is in fact hardest to obtains are the solutions of the
system or, occasionally, some specific solutions. This work is based on a most
enlightening M\'emoire written by \'Elie Cartan in 1914 and that the majority
ignores. We discuss a setting for the local equivalence problem and illustrate
it by some examples. It should also be noted that any integration process or
method is in fact a local equivalence problem involving a suitable model.
