All planar quadratic and cubic quasi-homogeneous non-homogeneous polynomial systems are shown to reduce to three homogeneous systems, and their global phase portraits are classified into a finite list of topological types.
P´ erez del R ´ ıo, Planar quasi-homogeneous poly- nomial differential systems and their integrability, Journal of Differential Equations 255 (2013), 3185–3204
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Global Dynamics Of Quadratic And Cubic Planar Quasi-homogeneous Differential Systems
All planar quadratic and cubic quasi-homogeneous non-homogeneous polynomial systems are shown to reduce to three homogeneous systems, and their global phase portraits are classified into a finite list of topological types.