The Hoyer polynomial differential systems depend on nine parameters. We provide the necessary conditions in order that these systems have two functionally independent polynomial first integrals. We show that these conditions are not sufficient. Additionally, we illustrate how the polynomial first integrals of these systems can be computed using the Kowalevsky exponents. © 2012 Elsevier Ltd.
- Homogeneous differential systems
- Hoyer systems
- Polynomial first integrals