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A family of non-darboux-integrable quadratic polynomial differential systems with algebraic solutions of arbitrarily high degree

✍ Scribed by J. Chavarriga; M. Grau


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
361 KB
Volume
16
Category
Article
ISSN
0893-9659

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✦ Synopsis


we show that the system S = 1, B = 2n + 2sy + y2 has the algebraic solution h(z, v) = Zf,,(z)y + 2nH,,-i(r),

where'H,,(r) is the Hermite polynomial of degree n, and the system is not Darboux integrable and has no Darboux integrating factor for any n E N.