Journals Information
Universal Journal of Applied Mathematics Vol. 2(2), pp. 109 - 118
DOI: 10.13189/ujam.2014.020206
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Analytical Solutions of the Riccati Equation with Coefficients Satisfying Integral or Differential Conditions with Arbitrary Functions
Tiberiu Harko 1,*, Francisco S. N. Lobo 2, M. K. Mak 3
1 Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
2 Centro de Astronomia e Astrof sica da Universidade de Lisboa, Campo Grande, Ed. C8 1749-016 Lisboa, Portugal
3 Department of Computing and Information Management,Hong Kong Institute of Vocational Education,Chai Wan, Hong Kong, P. R. China
ABSTRACT
Ten new exact solutions of the Riccati equation dy/dx = a(x) + b(x)y + c(x)y2 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 appropriately 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 for the Riccati equation. For each case the general solution of the Riccati equation is also presented. The possibility of the application of the obtained mathematical results for the study of anisotropic general relativistic stellar models is also briefly considered.
KEYWORDS
Riccati Equation, Integrability Condition, Exact Solutions: Anisotropic Relativistic Stellar Models, Stars
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Tiberiu Harko , Francisco S. N. Lobo , M. K. Mak , "Analytical Solutions of the Riccati Equation with Coefficients Satisfying Integral or Differential Conditions with Arbitrary Functions," Universal Journal of Applied Mathematics, Vol. 2, No. 2, pp. 109 - 118, 2014. DOI: 10.13189/ujam.2014.020206.
(b). APA Format:
Tiberiu Harko , Francisco S. N. Lobo , M. K. Mak (2014). Analytical Solutions of the Riccati Equation with Coefficients Satisfying Integral or Differential Conditions with Arbitrary Functions. Universal Journal of Applied Mathematics, 2(2), 109 - 118. DOI: 10.13189/ujam.2014.020206.