| 二阶微分方程为全微分方程的充要条件及其求解 |
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| 引用本文： | 甘华来. 二阶微分方程为全微分方程的充要条件及其求解[J]. 各界, 2008, 0(8) |
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| 作者姓名： | 甘华来 |
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| 作者单位： | 安徽省合肥学院数学与物理系; |
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| 基金项目： | 安徽省教育厅教研项目:新建本科院校应用型人才培养模式下数学专业分层教学的探索与实践的课题资助 |
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| 摘 要： | 给出形如f(x)d~2x/dt~2+g(dx/dt)~n=0(其中f(x),g(x)在公共定义域上连续且f(x)可导)的二阶微分方程为全微分方程的充要条件及其通解结构,以及当n=2时积分因子的找法,再给出了几类可化为d~2x/dt~2+g(dx/dt)~n=2=0型的高阶微分方程,最后举例说明如何运用。
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| 关 键 词： | 二阶微分方程 全微分方程 积分因子 |
Second-order differential equation for total differential equation necessary and sufficient condition and solution |
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| Gan Hualai. Second-order differential equation for total differential equation necessary and sufficient condition and solution[J]. All Circles, 2008, 0(8) |
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| Authors: | Gan Hualai |
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| Affiliation: | Department of Mathenatics and Physics;Hefei University;2006 levels of information and computing science specialties |
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| Abstract: | Gives the shape like f(x)d~2x/dt~2+g(x)(dx/dt)~n=0(f(x),g(x)in public domain of definition and f(x)may lead continuously)second-order differential equation for total differential equation necessary and sufficient condition and ordinary solution structure,as well as,when n=2 the integrating factor looks for the law,gave several kinds to be possible again to change into thef(x)d~2xdt~2+g(x)(dx/dt)~2=0 higher order differential equation,how finally explained with examples to utilize. |
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| Keywords: | Second-order differential equation Total differential equation Integrating factor |
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