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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Elementary first integrals of differential equations
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by M. J. Prelle and M. F. Singer PDF
Trans. Amer. Math. Soc. 279 (1983), 215-229 Request permission

Abstract:

We show that if a system of differential equations has an elementary first integral (i.e. a first integral expressible in terms of exponentials, logarithms and algebraic functions) then it must have a first integral of a very simple form. This unifies and extends results of Mordukhai-Boltovski, Ritt and others and leads to a partial algorithm for finding such integrals.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 279 (1983), 215-229
  • MSC: Primary 12H05
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0704611-X
  • MathSciNet review: 704611