| 三类新的高阶非线性常微分方程的求解定理 |
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| 引用本文： | 汤光宋. 三类新的高阶非线性常微分方程的求解定理[J]. 五邑大学学报(自然科学版), 2001, 15(4): 37-42 |
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| 作者姓名： | 汤光宋 |
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| 作者单位： | 江汉大学数学系, |
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| 摘 要： | 采用函数迭代法，给出一个引理，提出三类新的高阶非线性常微分方程，反复利用函数的迭代使之转化为微分方程组的求解，再应用积分法，以获得原微分方程的通积分公式，从而论证了方程的可积性，直接运用通积分公式，使得求解相应方程的解的过程大为简化。
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| 关 键 词： | 高阶非线性常微分方程 函数迭代法 微分方程组 积分法 通积分公式 求解定理 |
| 文章编号： | 1006-7302(2001)04-0037-06 |
| 修稿时间： | 2000-06-05 |
Theorems of Solving Three New Types of Higher DegreeNonlinear Ordinary Differential Equations |
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| TANG Guang-song. Theorems of Solving Three New Types of Higher DegreeNonlinear Ordinary Differential Equations[J]. Journal of Wuyi University(Natural Science Edition), 2001, 15(4): 37-42 |
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| Authors: | TANG Guang-song |
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| Abstract: | In this paper, using the method of function iteration, a lemma was given, and three new types of higher degree nonlinear ordinary differential equations were presented. Using the method one and again the equations can be translated linear differential equation system and be solved. And then using the method of integral, general integral formula can be obtained, so that the integrability of original equations can be proved. Diretly using general integral formula, the proess of solving equations can be greatly simplified. |
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| Keywords: | nonlinear higher degree differential equation method of function iteration equation system integral method general integral formula |
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