The Classification of Time Invariants (First Integrals) of Multinomial Systems of O.D.E.s and the Surprising Link Between Algebraic and Logarithmic Time Invariants, Dictated by the Method of Arrays

Abstract

For a large class of systems of o.d.e.'s which have first integrals, the method of arrays yields the following results: i) The first integrals $I$ can be found by solving systems of linear equations. ii) How the first integral $I$ responds to changes in the system $S$. iii) An easy way for finding the first integral for a special class of first integrals if they exist.