Analytical Solutions of the Riccati Equation with Coefficients Satisfying Integral or Differential Conditions with Arbitrary Functions

@article{Harko2014AnalyticalSO,
  title={Analytical Solutions of the Riccati Equation with Coefficients Satisfying Integral or Differential Conditions with Arbitrary Functions},
  author={Tiberiu Harko and Francisco S. N. Lobo and M. K. Mak},
  journal={Universal Journal of Applied Mathematics},
  year={2014},
  volume={2},
  pages={109-118}
}
Ten new exact solutions of the Riccati equation dy/dx = a(x) + b(x)y + c(x)y 2 are presented. The solutions are obtained by assuming certain relations among the coefficients a(x), b(x) and c(x) of the Riccati equation, in the form of some integral or differential expressions, also involving some arbitrary functions. By ap- propriately choosing the form of the coefficients of the Riccati equation, with the help of the conditions imposed on the coefficients, we obtain ten new integrability cases… Expand
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