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<cfResPublDate>2023-12-30</cfResPublDate>
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<cfTitle cfLangCode='EN' cfTrans='o'>First integrals in a cubic differential system with one invariant straight line and one invariant cubic</cfTitle>
<cfKeyw cfLangCode='EN' cfTrans='o'>Cubic differential system; invariant algebraic curve; Darboux integrability; The problem of the center; sistem diferențial cubic; curbă algebrică invariantă; integrabilitatea Darboux; problema centrului și focarului</cfKeyw>
<cfAbstr cfLangCode='EN' cfTrans='o'><p>In this paper we find conditions for a singular point ?(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 ?(0, 0) is proved by constructing Darboux first integrals.</p></cfAbstr>
<cfAbstr cfLangCode='RO' cfTrans='o'><p>&Icirc;n lucrare se examinează sistemul diferențial cubic cu punctul singular <!--[if gte msEquation 12]><m:oMath><i
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</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[endif]-->&nbsp;de tip centru sau focar, care are o dreaptă invariantă și o cubică invariantă. Pentru acest sistem sunt determinate condițiile de existență a centrului &icirc;n <!--[if gte msEquation 12]><m:oMath><i
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