Geodesic
Explicitly solvable systems of first-order ordinary differential equations with homogeneous right-hand sides, and their periodic variants
Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 1, pp. 5-19

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In this paper we identify systems of an arbitrary number $N$ of first-order Ordinary Differential Equations with nonlinear homogeneous right-hand sides of an arbitrary (integer, positive or nonpositive) degree $M$, which feature very simple explicit solutions; as well as variants of these systems—with right-hand sides no more homogeneous—some of which feature periodic solutions. A novelty of these findings is to consider systems characterized by constraints involving their parameters and/or their initial data.
Keywords: explicitly solvable dynamical systems, solvable systems of first-order ODEs, isochronous dynamical systems. 
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     title = {Explicitly solvable systems of first-order ordinary differential equations with homogeneous right-hand sides, and their periodic variants},
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F. Calogero; F. Payandeh. Explicitly solvable systems of first-order ordinary differential equations with homogeneous right-hand sides, and their periodic variants. Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 1, pp. 5-19. http://geodesic.mathdoc.fr/item/TMF_2022_213_1_a0/