Integrabilitatea Darboux pentru sistemele diferențiale cubice ce posedă trei drepte invariante reale în poziție generică a căror multiplicitate totală este egală cu șase împreună cu dreapta de la infinit

Abstract

Consider the general cubic differential system x & = P(x, y), y & = Q(x, y) , where P Q x y , , E [ ], max deg ,deg 3 { P Q} = ,GCD P Q ( , 1 ) = . According to [1], a differential system is Darboux integrable if this system has sufficiently many invariant straight lines considered with their multiplicities. In this paper we obtain 2 canonical forms of cubic differential systems which possess three real invariant straight lines in generic position of total multiplicity seven including the straight line at the infinity. Moreover, we compute their Darboux integrating factors.