On a Liouville Integrable Planar Differential System with Non-Algebraic Limit Cycle

Abstract

In this paper, we prove that a class of differential system of degree nine is Liouville integrable by transforming it into a Bernoulli differential equation and we determine exactly its first integral. This allows us to show that this class admits an explicit non-algebraic limit cycle enclosing the origin, here a non-elementary singular point. For singularities, at infinity, this class does not possess singular points.