General solutions depending algebraically on arbitrary constants
Source: Nagoya Math. J. Volume 113 (1989), 1-6.
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Primary Subjects: 12H05
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Links and Identifiers
 T. Kimura, On conditions for ordinary differential equations of the first order to be reducible to a Riccati equation by a rational transformation, Funkcial. Ekvac, 9 (1966), 251-259.
 E. R. Kolchin, Differential Algebra and Algebraic Groups, Academic Press, New York, 1973.
 M. Matsuda, First order algebraic differential equations, A differential algebraic approach, Lecture Notes in Math.,04, Springer, Berlin, 1980.
 K. Nishioka, A theorem of Painleve on parametric singularities of algebraic differ- ential equations of the first order, Osaka J. Math., 18 (1981),
 K. Nishioka, A note on the transcendency of Panleve's first transcendent,Nagoya Math.J., 109 (1988), 63-67.
[Q] Differential algebraic function fields depending rationally on arbitrary con- stants, Nagoya Math. J., 113 (1989), 173-179.
 P. Painleve, Leon de Stockholm, OEuvres de P. Painleve I, 199-818, Editions du C.N.R.S., Paris, 1972.
 H. Umemura,Birational automorphism groups and differential equations,to appear.
 H. Umemura, On the irreducibility of the first differential equation of Painleve, in preprint. Takabatake-cho, 18-632 Nara 630, Japan
Mathematical Reviews (MathSciNet): MR977782