  We generalize the classical Lie results on a basis of differential invariants
for a one-parameter group of local transformations to the case of arbitrary
number of independent and dependent variables. It is proved that if universal
invariant of a one-parameter group is known then a complete set of functionally
independent differential invariants can be constructed via one quadrature and
differentiations. Some applications of first-order differential invariants to
Riccati-type systems are also presented.
