Nishioka, Keiji General solutions depending algebraically on arbitrary constants. (English) Zbl 0702.12008 Nagoya Math. J. 113, 1-6 (1989). 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 Cited in 2 ReviewsCited in 4 Documents MSC: 12H20 Abstract differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations Keywords:algebraic differential equations; differential fields; algebraic dependence; moving singularities Citations:Zbl 0462.12009 PDFBibTeX XMLCite \textit{K. Nishioka}, Nagoya Math. J. 113, 1--6 (1989; Zbl 0702.12008) Full Text: DOI 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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.