  A. Gasull shared a list of 33 open problems in low dimensional dynamical
systems in his work in 2021. The second part of Problem 3 is about whether the
limit cycle of a quasi-homogeneous system $
  \dot{x}=y,\;
  \dot{y}=-x^3+\alpha x^2y+y^3 $ is unique. In this paper, we give a positive
answer to this question by analysing the uniqueness of the heteroclinic
separatrix at infinity.
