| 广义Riccati方程可积的充要条件及其推广 |
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| 引用本文： | 段锋,赵临龙,张兰. 广义Riccati方程可积的充要条件及其推广[J]. 河南科学, 2013, 0(10): 1580-1586 |
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| 作者姓名： | 段锋 赵临龙 张兰 |
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| 作者单位： | [1]常德职业技术学院,湖南常德415000 [2]安康学院数学与应用数学研究所,陕西安康725000 |
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| 基金项目： | 湖南省教育厅科学研究项目（13c007） |
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| 摘 要： | 利用变量代换的方法,讨论了广义Riccati方程的一个可积的充要条件,提仁0出了可通过分离变量求解的广义Riccati方程的一般形式,推广了其可积性定理,提供了其可积性讨论的新方法．
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| 关 键 词： | 广义Riccati方程 分离变量 变量代换 二项式定理 可积性 充要条件 |
The Necessary and Sufficient Conditions of the Generalized Riccati Equation Integrability and Its Inference |
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| Duan Feng,Zhao Linlong,Zhang Lan. The Necessary and Sufficient Conditions of the Generalized Riccati Equation Integrability and Its Inference[J]. Henan Science, 2013, 0(10): 1580-1586 |
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| Authors: | Duan Feng Zhao Linlong Zhang Lan |
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| Affiliation: | 1 (1. Changde Vocationa! Technical College, Changde 415000, Hunan China; 2. Mathematics and Applied Mathematics School, Ankang University, Ankang 725000, Shaanxi China) |
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| Abstract: | Application of variable substitution method, the authors discuss the necessary and sufficient conditions of the generalized Riccati differential equation integrability, put forward the general form of this type Riccati equation that can be solved via the approach of separating variables. The paper provides a new method of discussing the integrability of this diferential equations. |
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| Keywords: | the generalized Riccati differential equation separating-variables variable substitution： binomialtheorem： integrability： necessary and sufficient conditions |
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