  We argue that the Mellin-Barnes representations of Feynman diagrams can be
used for obtaining linear systems of homogeneous differential equations for the
original Feynman diagrams with arbitrary powers of propagators without recourse
to the integration-by-parts technique. These systems of differential equations
can be used (i) for the differential reductions to sets of basic functions and
(ii) for counting the numbers of master integrals.
