In the geometry of generic 2-plane fields on 5-manifolds, the local equivalence problem was solved by Cartan who also constructed the fundamental curvature invariant. For generic 2-plane fields or (2, 3, 5)-distributions determined by a single function of the form F (q), the vanishing condition for the curvature invariant is given by a 6 order nonlinear ODE. Furthermore, An and Nurowski showed ...