Real two-dimensional homogeneous cubic systems of ODE, polynomials in the right-hand part of which have a common linear factor are considered. On the basis of properly introduced ordering principles, the set of these systems is divided into classes of linear equivalence, in each of which the structurally simplest system is distinguished the normal form of the third order.
For the coe cient matrix of its right-hand side, called the canonical form (CF), the canonical set of values is speci ed, which guarantees the system a liation to the selected class. In addition, for each CF a) conditions on the coe cients of the original system, b) linear substitutions that reduce the right-hand part of the system under these conditions to the chosen CF, c) obtained values of CF coe cients are given. In existing applications programs written using the Maple software are presented, which allowed us to obtain the majority of practical results. Refs 4.