{
  "id": "1301.5720",
  "version": "v2",
  "published": "2013-01-24T07:15:09.000Z",
  "updated": "2014-03-26T07:35:45.000Z",
  "title": "New further integrability cases for the Riccati equation",
  "authors": [
    "M. K. Mak",
    "T. Harko"
  ],
  "comment": "7 pages, no figures, accepted for publication in Applied Mathematics and Computation; featured in Advances in Engineering, http://advancesENG.com/",
  "journal": "Applied Mathematics and Computation 219 (2013), pp. 7465-7471",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "New further integrability conditions of the Riccati equation $dy/dx=a(x)+b(x)y+c(x)y^{2}$ are presented. The first case corresponds to fixed functional forms of the coefficients $a(x)$ and $c(x)$ of the Riccati equation, and of the function $F(x)=a(x)+[f(x)-b^{2}(x)]/4c(x)$, where $f(x)$ is an arbitrary function. The second integrability case is obtained for the \"reduced\" Riccati equation with $b(x)\\equiv 0$. If the coefficients $a(x)$ and $c(x)$ satisfy the condition $\\pm d\\sqrt{f(x)/c(x)}/dx=a(x)+f(x)$, where $f(x)$ is an arbitrary function, then the general solution of the \"reduced\" Riccati equation can be obtained by quadratures. The applications of the integrability condition of the \"reduced\" Riccati equation for the integration of the Schr\\\"odinger and Navier-Stokes equations are briefly discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-26T07:35:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riccati equation",
      "arbitrary function",
      "integrability condition",
      "second integrability case",
      "first case corresponds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.5720M"
    }
  }
}