Explicit Non Algebraic Limit Cycle for a Discontinuous Piecewise Differential Systems Separated by One Straight Line and Formed by Linear Center and Linear System Without Equilibria

In this paper, we deal with the discontinuous piecewise differential linear systems formed by two differential systems separated by a straight line when one of these two differential systems is a linear without equilibria and the other is a linear center. We are going to show that the maximum number of crossing limit cycles is one, and if exists, it is non algebraic and analytically given.