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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

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