Abstract
We give necessary and sufficient conditions for the complete integrability of first order N–dimensional differential systems.We propose a new method to determine in the Jacobi Theorem the last N−1 first integral for the complete integrability of an N–dimensional differential system with N−2 independent first integrals and with a Jacobi multiplier.As an application we study the complete integrability of some 3–dimensional differential systems, more precisely the complete integrability of the asymmetric and symmetric May–Leonard differential systems.
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