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SM ISO690:2012 BALTAG, Valeriu, CALIN, Iurie. The transvectants and the integrals for Darboux systems of differential equations. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2008, nr. 1(56), pp. 4-18. ISSN 1024-7696. |
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
Numărul 1(56) / 2008 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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Pag. 4-18 | ||||||
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We apply the algebraic theory of invariants of differential equations to integrate the polynomial differential systems dx/dt = P1(x, y) xC(x, y), dy/dt = Q1(x, y) y C(x, y), where real homogeneous polynomials P1 and Q1 have the first degree and C(x, y) is a real homogeneous polynomial of degree r ≥ 1. In generic cases the invariant algebraic curves and the first integrals for these systems are constructed. The constructed invariant algebraic curves are expressed by comitants and invariants of investigated systems. |
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