Various methods of integrability of cubic differential systems with real invariant lines of multiplicity eight

Abstract

In this article, we study cubic planar differential systems with affine real invariant straight lines of total multiplicity eight. For these differential systems (there are 24 differential systems) the integrability problem is solved by various methods: the Darboux method, the direct method and the computational method. The results obtained by these three methods coincide, i.e. the obtained solutions are equivalent to each other or they differ from each other by an integration constant.