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General solutions depending algebraically on arbitrary constants. (English) Zbl 0702.12008

The author’s theorem [Osaka J. Math. 18, 249-255 (1981; Zbl 0462.12009)] about the algebraic dependence of the general solution to a first order algebraic ordinary differential equation upon those of equations free from moving singularities is generalized to the higher order case. This improves a result of P. Painlevé [Oevres, Vol. 1, 199-818 (Paris, 1973)].
Reviewer: S.V.Duzhin

MSC:

12H20 Abstract differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

Citations:

Zbl 0462.12009
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References:

[1] Lecture Notes in Math. #04 (1980)
[2] Differential Algebra and Algebraic Groups (1973)
[3] Funkcial. Ekvac 9 pp 251– (1966)
[4] Osaka J. Math. 18 (1981)
[5] Nagoya Math. J. 113 pp 173– (1989) · Zbl 0695.12016
[6] Nagoya Math. J. 109 (1988)
[7] OEuvres de P. Painlevé I pp 199– (1972)
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