Invariant algebraic curves linear in one variable for planar real quadratic systems

摘要

In this paper we study algebraic solutions of the form h(x,y)=p1(x)y+p2(x), where p1(x) and p2(x) are real coprime polynomials and p1(x)≠0, for a planar real algebraic quadratic system. We analyze the existence of this kind of solutions depending on the coefficients of the system.