| 一类特殊类型的Riccati方程的求解 |
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| 引用本文： | 张玮玮.一类特殊类型的Riccati方程的求解[J].安庆师范学院学报(自然科学版),2015(2):110-111. |
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| 作者姓名： | 张玮玮 |
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| 作者单位： | 安庆师范学院 数学与计算科学学院,安徽 安庆,246133 |
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| 基金项目： | 安徽省高等学校省级教学研究项目，安徽省高校自然科学研究一般项目(AQKJ2014B012)。 |
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| 摘 要： | Riccati方程在常微分方程中占有重要的位置。然而,对于一般形式的里卡蒂方程通解的求解一般没有初等解法,其解无法用初等函数或其积分表示。本文讨论了一类特殊类型的里卡蒂方程解的求解方法,并得出了其通解的公式,最后举例说明求这类方程的通解。
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| 关 键 词： | 微分方程 里卡蒂方程 特殊 通解 |
Discussion on the General Solutions of the Special Riccati Ordinary Differential Equations |
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| ZHANG Wei-wei.Discussion on the General Solutions of the Special Riccati Ordinary Differential Equations[J].Journal of Anqing Teachers College(Natural Science Edition),2015(2):110-111. |
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| Authors: | ZHANG Wei-wei |
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| Abstract: | Riccati equation is an important equation in the ordinary differential equations .However, for the soltions of the general Riccati ordinary differential equations, there is no elementary solution.The solution cannot be expressed in elementary function or integral.The general solutions of a special Riccati ordinary differential equations are discussed, and the formula of the general solution was obtained.Examples are given to illustrate the effectiveness in the end. |
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| Keywords: | ordinary differential equations Riccati special the general solutions |
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