Elementary first integrals of differential equations

Authors:
M. J. Prelle and M. F. Singer

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

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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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DOI:
https://doi.org/10.1090/S0002-9947-1983-0704611-X

Article copyright:
© Copyright 1983
American Mathematical Society