ABSTRACT
It is well known that every ordinary differential equation (ODE) of first order admits an infinite point group (e.g., see [107, 111]), but it is precisely in the case of first-order equations that a search for this group is ineffective. If the admissible symmetry is known, then an integrating factor for the ODE can be found explicitly (see the Introduction). Since the knowledge of the symmetry of a first-order ODE permits finding its general solution, we see that the construction of an invariant scheme does not make any practical sense. But it is of interest to find out what the relation between the symmetry and integrability is in the case of ordinary difference equations (see [120]).
