Abstract
This paper is concerned with the generalized Riccati equation R(m, n), and its special case, the classical Riccati equation R(2, 1). By the combination of Painlevé test and power series method, the Painlevé property is considered under the specific condition. Then, by the truncated expansion, the classical Riccati equation is reduced to a linear second-order ordinary differential equation. Furthermore, we give the exact analytic solution to the generalized Riccati equation, and the analytic solution to the classical Riccati equation is presented successively.
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This work was supported by the National Natural Science Foundation of China under Grant Nos. 11171041, 11401274, and the doctorial foundation of Liaocheng University under Grant No. 31805.
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Liu, H. Painlevé Analysis and Analytic Solutions to the Riccati Types of Equations. Results. Math. 68, 261–269 (2015). https://doi.org/10.1007/s00025-015-0438-2
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DOI: https://doi.org/10.1007/s00025-015-0438-2