| 一类二阶变系数非线性微分方程的通解及应用 |
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| 引用本文： | 冯录祥.一类二阶变系数非线性微分方程的通解及应用[J].三峡大学学报(自然科学版),2011,33(5):96-98. |
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| 作者姓名： | 冯录祥 |
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| 作者单位： | 宝鸡文理学院数学系,陕西宝鸡,721013 |
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| 基金项目： | 陕西省教育厅科研计划项目，宝鸡文理学院重点科研项目 |
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| 摘 要： | 根据一类二阶变系数非线性微分方程的特点,利用降阶法,给出了求其通解的一种简便方法,并得到了其通解公式,并在特殊情形下得到一系列可积的二阶变系数非齐次线性微分方程及其通解公式,进一步丰富了二阶变系数线性微分方程的可积理论.
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| 关 键 词： | 非线性微分方程 降阶法 通解 |
General Solution of Second Order Nonlinear Differential Equations with Variable Coefficients and Its Application |
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| Feng Luxiang.General Solution of Second Order Nonlinear Differential Equations with Variable Coefficients and Its Application[J].Journal of China Three Gorges University(Natural Sciences),2011,33(5):96-98. |
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| Authors: | Feng Luxiang |
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| Institution: | Feng Luxiang(Department of Mathematics,BaojiUniversity of Arts & Sciences,Baoji 721013,China) |
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| Abstract: | According to characteristics of the second order nonlinear differential equations with variable coefficients,the reduced-order method has been used;and then an easy way to find the general solution is given;meanwhile,the general solution formula has been obtained.Finally,a series of integrable second-order variable coefficient non-homogeneous linear differential equations and general solution formula in special circumstances has been received;furthermore the integrable theory of the second-order linear diff... |
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| Keywords: | nonlinear differential equations reduced-order method general solution |
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