✦ LIBER ✦
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
No coin nor oath required. For personal study only.
✦ 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.