{
  "id": "2104.03073",
  "version": "v1",
  "published": "2021-04-07T11:43:26.000Z",
  "updated": "2021-04-07T11:43:26.000Z",
  "title": "Explicitly solvable systems of two autonomous first-order Ordinary Differential Equations with homogeneous quadratic right-hand sides",
  "authors": [
    "Francesco Calogero",
    "Farrin Payandeh"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "After tersely reviewing the various meanings that can be given to the property of a system of nonlinear ODEs to be solvable, we identify a special case of the system of two first-order ODEs with homogeneous quadratic right-hand sides which is explicitly solvable. It is identified by 2 explicit algebraic constraints on the 6 a priori arbitrary parameters that characterize this system. Simple extensions of this model to cases with nonhomogeneous quadratic right-hand sides are also identified, including isochronous cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-07T11:43:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "autonomous first-order ordinary differential equations",
      "homogeneous quadratic right-hand sides",
      "explicitly solvable systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}