| 几类可化为新二阶变系数微分方程的可积判据 |
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| 引用本文： | 谭丹英.几类可化为新二阶变系数微分方程的可积判据[J].云南师范大学学报(自然科学版),2005,25(5):6-10. |
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| 作者姓名： | 谭丹英 |
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| 作者单位： | 临沧教育学院数学系,云南,临沧,677000 |
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| 摘 要： | 提出几类非线性微分方程,巧妙地借助线性化法、降阶法、交换变量位置法,将非线性微分方程转化为新的二阶变系数线性微分方程,在一定条件下,给出这几类非线性微分方程的可积性证明,提供了可积的判据及通解的表达式,并列举了实例。
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| 关 键 词： | 非线性微分方程 线性化法 降阶法 交换变量位置法 二阶变系数微分方程 可积判据 通解 |
| 文章编号： | 1007-9793（2005）05-0006-05 |
| 收稿时间： | 2004-09-02 |
| 修稿时间： | 2004-09-02 |
Integrable criterions of several types of new second-order linear variable-coefficient differential equations |
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| TAN Dan-ying.Integrable criterions of several types of new second-order linear variable-coefficient differential equations[J].Journal of Yunnan Normal University (Natural Sciences Edition),2005,25(5):6-10. |
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| Authors: | TAN Dan-ying |
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| Abstract: | In this paper several types of nonlinear differential equations are investigated and transmuted to new second-order linear variable-coefficient differential equations by employing linear transformation method, order reduction method, and exchange variables method dexterously. The integrability of these nonlinear differential equations are also proved within particular restricts. Then the integrable criterions and expressions of general solutions are given and some samples are suggested. |
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| Keywords: | nonlinear differential equations linear transformation method order reduction method exchange variables method second-order variable-coefficient differential equations integrable Criterions |
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