First integrals in a cubic differential system with one invariant straight line and one invariant cubic

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Keywords

cubic differential system
invariant algebraic curve
Darboux integrability
the problem of the center

How to Cite

Cozma, D. (2024). First integrals in a cubic differential system with one invariant straight line and one invariant cubic. Acta Et Commentationes Exact and Natural Sciences, 2(16), 97-105. https://doi.org/10.36120/2587-3644.v2i16.97-105

Abstract

In this paper we find conditions for a singular point O(0, 0) of a center or a
focus type to be a center, in a cubic differential system with one
invariant straight line and one invariant cubic. The presence of
a center at O(0, 0) is proved by constructing Darboux first
integrals.

https://doi.org/10.36120/2587-3644.v2i16.97-105
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