First integrals in a cubic differential system with one invariant straight line and one invariant cubic
Vol 16 No 2 (2023), Статьи
Vol 16 No 2 (2023)

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

Статьи
https://doi.org/10.36120/2587-3644.v16i2.97-105
Published January 17, 2024
Dumitru Cozma
"Ion Creangă" State Pedagogical University, 5 Gh. Iablocikin st., Chișinău, Republic of Moldova

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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, 16(2), 97-105. https://doi.org/10.36120/2587-3644.v16i2.97-105
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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.v16i2.97-105
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