2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56953We 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.12 pagesMathematical PhysicsDifferential GeometryGroup TheoryExactly Solvable and Integrable Systems53A55; 22E05; 58G35; 35A30; 34A34text