  We consider a classical problem of Computer Algebra: symbolic solution of
PDEs. We transform the famous Darboux theorems on differential transformations
of hyperbolic operator into the space of invariants. We introduce a new idea --
$X$- and $Y$-invariants of such operator as solutions of some equations written
in terms of the Laplace invariants of this operator. Explicit formula for the
changes in the sets of the $X$- and $Y$-invariants under the Darboux
transformations are obtained.
