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517.925 (42) |
Дифференциальные, интегральные и другие функциональные уравнения. Конечные разности. Вариационное исчисление. Функциональный анализ (243) |
SM ISO690:2012 REPEŞCO, Vadim. Canonical forms of cubic differential systems with real invariant straight lines of total multiplicity seven along one direction. In: Acta et commentationes (Ştiinţe Exacte și ale Naturii), 2018, nr. 2(6), pp. 124-132. ISSN 2537-6284. |
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Acta et commentationes (Ştiinţe Exacte și ale Naturii) | ||||||
Numărul 2(6) / 2018 / ISSN 2537-6284 /ISSNe 2587-3644 | ||||||
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CZU: 517.925 | ||||||
MSC 2010: 34C05 | ||||||
Pag. 124-132 | ||||||
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Consider the general cubic differential system x = P(x, y) , y =Q(x, y) , where [ ] ,,PQx y ÎR , { } max deg ,deg 3 P Q = , ( ) ,1GCDPQ= . If this system has enough invariant straight lines considered with their multiplicities, then, according to [1], we can construct a Darboux first integral. In this paper we obtain 26 canonical forms for cubic differential systems which possess real invariant straight lines along one direction of total multiplicity seven including the straight line at the infinity |
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Cuvinte-cheie Cubic differential system, invariant straight line, Darboux integrability, sistem diferențial cubic, dreaptă invariantă, integrabilitate Darboux |
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