Classification of certain types of underdetermined systems of ordinary differential equations (Q610560)

Consider a system of differenial equations of the form \[ \sum_{i=1}^{n}g_i^k(y)\frac{dy^i}{dt}+g_{n+1}^k(y)=0, \] where \(k=1,\dots,q\) and \(q<n\). Two systems of that form are called equivalent if they are conjugated by a diffeomorphism. The author gives lists of possible simple equivalent systems for \(q=1\) and for \(q=2,n=3\). No proofs are given.