caa a22 4500 60620105X CHVBK 20210128100946.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00025-015-0438-2 doi (NATIONALLICENCE)springer-10.1007/s00025-015-0438-2 Liu Hanze School of Mathematical Sciences, Liaocheng University, 252059, Liaocheng, Shandong, China aut Painlevé Analysis and Analytic Solutions to the Riccati Types of Equations [Elektronische Daten] [Hanze Liu] 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. Springer Basel, 2015 Riccati equation nationallicence Painlevé test nationallicence power series method nationallicence analytic solution nationallicence Results in Mathematics Springer Basel 68/1-2(2015-09-01), 261-269 1422-6383 68:1-2<261 2015 68 25 https://doi.org/10.1007/s00025-015-0438-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00025-015-0438-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Liu Hanze School of Mathematical Sciences, Liaocheng University, 252059, Liaocheng, Shandong, China aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 68/1-2(2015-09-01), 261-269 1422-6383 68:1-2<261 2015 68 25