| 变系数微分方程的常系数化条件 |
| |
| 引用本文： | 宋和平,李军红,崔宁. 变系数微分方程的常系数化条件[J]. 河北科技师范学院学报, 2006, 20(2): 4-7 |
| |
| 作者姓名： | 宋和平 李军红 崔宁 |
| |
| 作者单位： | 河北科技师范学院,数理系,河北,秦皇岛,066004;河北建筑工程学院,教务处 |
| |
| 摘 要： | 不同于解具有e∫φ(z)dz形式的待定函数法,由引理1给出了n阶变系数微分方程具体的因变量代换形式,从而给出n阶变系数微分方程常系数化的充要条件并加以详细证明,由此得到二阶、三阶变系数线性微分方程常系数化的充要条件,同时指出三阶变系数微分方程在具体应用中令a1=0的简便性.对二阶变系数非线性微分方程的常系数化给出两个使其可积的条件,并举例论证.
|
| 关 键 词： | 变系数方程 常系数化 变量代换 |
| 文章编号： | 1672-7983(2006)02-0004-04 |
| 修稿时间： | 2005-06-24 |
The Constant Coefficient Condition of Differential Equation with Variable Coefficient |
| |
| SONG He-ping,LI Jun-hong,CUI Ning. The Constant Coefficient Condition of Differential Equation with Variable Coefficient[J]. Journal of Hebei Normal University of Science & Technology, 2006, 20(2): 4-7 |
| |
| Authors: | SONG He-ping LI Jun-hong CUI Ning |
| |
| Abstract: | The constant coefficient condition of n differential equation with variable coefficient is given and expounded,the complexion of the second order and the third order is acquired,and the simplicity of third order differential equation with variable coefficient being applied with is pointed out as well.The two conditions of the second order nonlinear differential equation with variable coefficient are given and expounded with examples. |
| |
| Keywords: | equation with variable coefficient constant coefficient variable substitution |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
