Extended Prelle–Singer procedure and Darboux polynomial method: An unknown interconnection

Abstract

In this work, we present a new systematic procedure to derive two integrals from a Darboux polynomial for the given second order nonlinear ordinary differential equation (ODE). We succeed it by exploring an interlink between Darboux polynomial (DP) and the extended Prelle–Singer procedure (PS) quantities, namely null forms and integrating factors. We demonstrate the interconnection with suitable examples.