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Solutions of Riccati-Abel equation in terms of third order trigonometric functions

Author

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  • Robert M. Yamaleev

    (Laboratory of Informational Technologies)

Abstract

Solutions of the generalized Riccati equations with third order nonlinearity, named as Riccati-Abel equation, are expressed via third order trigonometric functions. It is shown, as the ordinary Riccati equation, also the Riccati-Abel equation has a relationship with a linear differential equations. A summation formula for solutions of Riccati-Abel equation is established. Possible applications of this formula in the generalized dynamics is outlined. The method admits an extension to the case of generalized Riccati equations with any order of nonlinearity

Suggested Citation

  • Robert M. Yamaleev, 2014. "Solutions of Riccati-Abel equation in terms of third order trigonometric functions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(2), pages 165-184, April.
    • Handle: RePEc:spr:indpam:v:45:y:2014:i:2:d:10.1007_s13226-014-0057-8
    DOI: 10.1007/s13226-014-0057-8
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    Cited by:

    1. Antoni Ferragut & Jaume Llibre, 2020. "On the Polynomial Solutions of the Polynomial Differential Equations y y′ = a0(x) + a1(x) y + a2(x) y2 + … + an(x) yn," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 217-232, March.

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