| 微分方程中一些新的可积类型 |
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| 引用本文： | 冯兆生,张玉明. 微分方程中一些新的可积类型[J]. 北京交通大学学报(自然科学版), 1997, 0(2) |
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| 作者姓名： | 冯兆生 张玉明 |
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| 作者单位： | 北方交通大学数学系(冯兆生)，辽宁商业高等专科学校(张玉明) |
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| 摘 要： | 一般的Ｒｉｃｃａｔｉ方程和二阶变系数方程是不可积的，本文主要利用构造微分方程线性算子，得到了微分方程的算子矩阵，从这个算子矩阵列向量的线性相关性，得到了Ｒｉｃｃａｔｉ方程和二阶变系数方程的一些新的可积类型，并举例说明以往一些文献中收集的相应部分的可积方程几乎全是本文的特例
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| 关 键 词： | 微分方程 可积性 线性算子 矩阵 线性相关 |
On Some New Integrable Types of Differential Equations |
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| Feng Zhaosheng. On Some New Integrable Types of Differential Equations[J]. JOURNAL OF BEIJING JIAOTONG UNIVERSITY, 1997, 0(2) |
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| Authors: | Feng Zhaosheng |
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| Abstract: | As we know, the general Riccati equation and second-order linear differential equation with varying coefficients are not integrable. In the present present paper, by constructing the linear operator of differential equation and establishing the operator matrixes, we obtain some new integrable types for Riccati equations and second-order differential equations, and give the examples to illustrate that almost all the corresponding intehgrable equations collected in some works in the past are the particular cases of theorems in this paper. |
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| Keywords: | differential equation integrability linear operator matrix linear dependence |
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