Here we study quadratic systems using certain Dulac functions and a geometric method.

In this report we present the generalization of a solution to Einstein’s equations with perfect fluid for the case of Einstein-Maxwell with perfect fluid. The effect of the charge is reflected by a parameter, ν, its interval is determined by the positivity condition from the pressure in the interior of the star. It is shown that the solution is stable according to the Zeldovich criteria as well as in relation to the criteria of the adiabatic index. The compactness, u = GM/c2R, of this charged model is greater that for the chargeless case, as a result of the effect from the presence of the charge. Which allows to represent stars with a high compactness, in particular a graphic analysis is presented for the star SAX J1808.4-3658 with mass M = 1.435M⊙ and radius R = 7.07km, from these data and employing the solution we obtain that the total maximum charge for the star is Q = 2.4085 × 1020C.

In this paper we make an analysis of a generalization of van der Pol equation without periodic orbits in a domain on the plane. We use a Gasull's result and Dulac's criterion. Mathematics Subject Classification: 34A34