{
  "id": "2106.06634",
  "version": "v1",
  "published": "2021-06-11T23:12:57.000Z",
  "updated": "2021-06-11T23:12:57.000Z",
  "title": "Explicitly Solvable Systems of First-order Ordinary Differential Equations with Polynomial Right-hand Sides, and Their Periodic Variants",
  "authors": [
    "Francesco Calogero",
    "Farrin Payandeh"
  ],
  "comment": "4 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this Letter we identify special systems of (an arbitrary number) N of first-order Ordinary Differential Equations with homogeneous polynomials of arbitrary degree M on their right-hand sides, which feature very simple explicit solutions; as well as variants of these systems--with right-hand sides no more homogeneous--which feature periodic solutions. A novelty of these findings is to consider special systems characterized by constraints involving both their parameters and their initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-11T23:12:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first-order ordinary differential equations",
      "polynomial right-hand sides",
      "explicitly solvable systems",
      "periodic variants",
      "special systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}