| 一类新二阶非线性微分方程的可积判据 |
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| 引用本文： | 张学元.一类新二阶非线性微分方程的可积判据[J].南阳师范学院学报,2004,3(3):15-18. |
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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： | 先通过类比名的Bernoulli方程，提出了一类新二阶非线性微分方程，然后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达式；在退化情形下，导出了经典的二阶常系数线性非齐次微分方程的通解表达式及二阶变系数线性齐次微分方程的一个新的可积类型。
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| 关 键 词： | 非线性微分方程 Bernoulli方程 通解 可积判据 特征方程 |
| 文章编号： | 1671-6132(2004)03-0015-04 |
| 修稿时间： | 2003年11月16 |
Integral Criterion of One Kind of New Second Order Non-Linear Differiential Equation |
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| ZHANG Xue-yan.Integral Criterion of One Kind of New Second Order Non-Linear Differiential Equation[J].Journal of Nanyang Teachers College,2004,3(3):15-18. |
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| Authors: | ZHANG Xue-yan |
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| Abstract: | Analogizing the famous Berroulli Equation,one kind of new second order non-linear differiential equation is given.And then,the concept of characteristic equation is introduced,a practical,integral,Sufficient criterion and the integral expression of its general solution for this equation is given.Particularly,the expression of the general solution for the classical second constant coefficient linear non-homogeneous differential equation and a new integral type for the second order variable coefficient linear homogeneous differential equation are deduced. |
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| Keywords: | a new second order non-linear differential equation characteristic equation integral criterion integral (expression) of the general solution |
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