On structure-preserving point transformations of differential equations

We apply a novel method for the equivalence group and its infinitesimal generators to the investigation of invariants of ODEs. First, a comparative study of this method is illustrated by an example. Next, the method is used to obtain invariants of low order linear ODEs, and the equivalence transformations for an arbitrary order of these equations. Other properties of the equations are also obtained, including the exact number of their invariants.