| 新二阶非线性微分方程的求解定理 |
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| 引用本文： | 张学元.新二阶非线性微分方程的求解定理[J].长沙大学学报,2004,18(4):8-13. |
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| 作者姓名： | 张学元 |
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| 作者单位： | 湖南工程学院数理系,湖南,湘潭,411104 |
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| 摘 要： | 提出了一类新二阶非线性微分方程,对它引进特征方程的概念,给出了一个实用的可积充分判据及其通解的积分表述式,在退化情形下,导出了两类新二阶变系数线性微分方程的求解定理,所得结果扩大了常微分方程的求解范围.
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| 关 键 词： | 新二阶非线性微分方程 新二阶变系数线性微分方程 特征方程 可积判据 通解的积分表达式 |
| 文章编号： | 1008-4681(2004)04-0008-06 |
Solution Seeking Formula of New Second Order Non-Linear Differential Eguation |
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| ZHANG Xueyuan.Solution Seeking Formula of New Second Order Non-Linear Differential Eguation[J].Journal of Changsha University,2004,18(4):8-13. |
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| Authors: | ZHANG Xueyuan |
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| Abstract: | In this paper, one kind of new secand order non-linear differential equation is given. And then, the concept of chaxacteristic equation is introduced, a practical, integral, sufficient criterion and the integral expression of the general solution for this equation is given. Particularly the solution seeking formula of the two kind new second order variable coefficient linear differential equation are deduced. The conclusions drawn expands the scope of solutions to differential equations. |
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| Keywords: | new second order non-linear differential equation new second order variable coefficient linear differential equation charactenistic equation integral eriterion integral expression of the general solution |
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