Nagoya Mathematical Journal

General solutions depending algebraically on arbitrary constants

Keiji Nishioka

Full-text: Open access

Article information

Nagoya Math. J. Volume 113 (1989), 1-6.

First available in Project Euclid: 14 June 2005

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 12H05: Differential algebra [See also 13Nxx]


Nishioka, Keiji. General solutions depending algebraically on arbitrary constants. Nagoya Math. J. 113 (1989), 1--6.

Export citation


  • [1] 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.
  • [2] E. R. Kolchin, Differential Algebra and Algebraic Groups, Academic Press, New York, 1973.
  • [3] M. Matsuda, First order algebraic differential equations, A differential algebraic approach, Lecture Notes in Math.,04, Springer, Berlin, 1980.
  • [4] K. Nishioka, A theorem of Painleve on parametric singularities of algebraic differ- ential equations of the first order, Osaka J. Math., 18 (1981),
  • [5] 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.
  • [7] P. Painleve, Leon de Stockholm, OEuvres de P. Painleve I, 199-818, Editions du C.N.R.S., Paris, 1972.
  • [8] H. Umemura,Birational automorphism groups and differential equations,to appear.
  • [9] H. Umemura, On the irreducibility of the first differential equation of Painleve, in preprint. Takabatake-cho, 18-632 Nara 630, Japan