Elementary first integrals of differential equations

Prelle, M. J.; Singer, M. F.

doi:10.1090/S0002-9947-1983-0704611-X

Elementary first integrals of differential equations
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by M. J. Prelle and M. F. Singer

Trans. Amer. Math. Soc. 279 (1983), 215-229

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

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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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