| 一类二阶变系数常微分方程的初等解法 |
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| 引用本文： | 梁洪亮,徐华伟. 一类二阶变系数常微分方程的初等解法[J]. 数学的实践与认识, 2009, 39(20) |
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| 作者姓名： | 梁洪亮 徐华伟 |
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| 作者单位： | 商丘师范学院,数学系,河南,商丘,476000 |
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| 基金项目： | 河南省2002年高校青年骨干教师资助计划项目、商丘师范学院重点学科资助项目 |
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| 摘 要： | 给出了一类二阶变系数常微分方程y″+pu(x)y′+[qu2(x)-ru′(x)]y=f(x)及y″+pu(x)y′+[qu2(x)-ru′(x)]y=f(x)[y-′ru(x)y]n可积的充分条件及其通解表达式,并举例说明它的一些简单应用.
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| 关 键 词： | 二阶变系数常微分方程 充分条件 特征方程 通解 |
The Elementary Solution of a Kind of Second Order Differential Equation with Variable Coefficient |
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| LIANG Hong-liang,XU Hua-wei. The Elementary Solution of a Kind of Second Order Differential Equation with Variable Coefficient[J]. Mathematics in Practice and Theory, 2009, 39(20) |
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| Authors: | LIANG Hong-liang XU Hua-wei |
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| Abstract: | A sufficient condition of a kind of second order differential equation with variable coefficienty"+pu(x)y'+[qu~2(x)-ru'(x)]y=f(x), andy"+pu(x)y'+[qu~2(x)-ru'(x)]y=f(x)[y'-ru(x)y]~n, and its general solution are given, and its explication is given by examples. |
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| Keywords: | the second order differential equation with variable coefficient sufficient conditions characteristic equation general solution |
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