Abstract In this paper we present the qualitative solution techniques of dynamic systems applied to the second order model of the synchronous machine (swing equation), with the aim of achieving a deeper analysis about the stability of the electric power system. Initially, the dynamics of the electrical power system are brief described, where the elements that interact in this and the stability classes to be analyzed are explained. Next, the mathematical model of the synchronous machine is formulated in detail from Newton‘s second law, in order to specify the theory of dynamic systems and the qualitative solutions that are applied to the study model. Finally, the results of the implementation of the qualitative solution techniques of the dynamic study system are presented, concluding with the stability zones of the synchronous machine.