| 高阶非线性常微分方程的可积类型 |
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| 引用本文： | 汤光宋 董巨清. 高阶非线性常微分方程的可积类型[J]. 应用数学和力学, 1991, 12(11): 1029-1036 |
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| 作者姓名： | 汤光宋 董巨清 |
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| 作者单位： | 1.江汉大学; |
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| 摘 要： | 本文借助于Leibniz公式、复合函数的高阶导数公式以及变量替换的方法,给出了较为广泛的高阶非线性常微分方程的可积类型,有的还提供了通积分的表达式.所得结论推广了文献中的结果.最后列举了实例.
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| 关 键 词： | 高阶非线性微分方程 可积类型 通积分 |
| 收稿时间： | 1990-06-11 |
Integrable Types of Nonlinear Ordinary Differential Equations of Higher-Orders |
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| Tane Guang-song. Integrable Types of Nonlinear Ordinary Differential Equations of Higher-Orders[J]. Applied Mathematics and Mechanics, 1991, 12(11): 1029-1036 |
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| Authors: | Tane Guang-song |
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| Affiliation: | 1.Jianghan University, Wuhan;2.Air Force Radar Academy, Wuhan |
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| Abstract: | In this paper,some integrable types of more general nonlinear ordinary differential equations of higher-orders are proposed in virtue of Leibniz formula, and formulas of higher-order derivatives of the composite functions as veil as substitution variables. The expressions for the general integrations of some of the equations are presented. The results obtained are the generalization of those in the references. Finally, some examples are also given. |
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| Keywords: | nonlinear differential equation of higher order integrable kind general integral |
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