A plane quadratic dynamical system is solved by using the perturbationincremental method. It is shown that there are only four cycles in the finite field of this system. Three of smaller amplitudes are the limit cycles (stability

instability and stability respectively) and the larger one is the homoclinic cycle. The untangent curve and the two gradual curves are plotted. The computation result showed that the perturbationincremental method is in good agreement compared with the numerical integral method. It is shown further that the number of the limit cycles of the planar polynomial differential systems (the second part of Hilbters 16 problems) cant be simply solved with using the algebra from the fact that there isnt the common point of intersection of the rate curves of the three limit cycles.