{
  "id": "1204.6546",
  "version": "v1",
  "published": "2012-04-30T04:03:24.000Z",
  "updated": "2012-04-30T04:03:24.000Z",
  "title": "New integrability case for the Riccati equation",
  "authors": [
    "M. K. Mak",
    "T. Harko"
  ],
  "comment": "10 pages, no figures, accepted for publication in Applied Mathematics and Computation",
  "journal": "Applied Mathematics and Computation 218 (2012), pp. 10974-10981",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "A new integrability condition of the Riccati equation $dy/dx=a(x)+b(x)y+c(x)y^{2}$ is presented. By introducing an auxiliary equation depending on a generating function $f(x)$, the general solution of the Riccati equation can be obtained if the coefficients $a(x)$, $b(x)$, $c(x)$, and the function $f(x)$ satisfy a particular constraint. The validity and reliability of the method are tested by obtaining the general solutions of some Riccati type differential equations. Some applications of the integrability conditions for the case of the damped harmonic oscillator with time dependent frequency, and for solitonic wave, are briefly discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-30T04:03:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riccati equation",
      "integrability case",
      "riccati type differential equations",
      "general solution",
      "integrability condition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1113222,
      "adsabs": "2012arXiv1204.6546M"
    }
  }
}