Binary differential equations with discriminant having a cusp singularity

Abstract

In this paper, we study binary differential equations (BDEs) with coefficients that vanish simultaneously at an isolated point and with discriminant having an A2-singularity at that point. We show that such BDEs can be grouped into three distinct types, and exhibit differences between these types in their codimension and the linear parts of their coefficients. We establish the topological configurations of the solution curves in each case with codimension ?4.