| 对一道微分方程通解的质疑 |
| |
| 引用本文： | 汪维刚. 对一道微分方程通解的质疑[J]. 高师理科学刊, 2011, 31(2): 54-55. DOI: 10.3969/j.issn.1007-9831.2011.02.016 |
| |
| 作者姓名： | 汪维刚 |
| |
| 作者单位： | 桐城师范高等专科学校,理工系,安徽,桐城,231402 |
| |
| 摘 要： | 利用常数变易法,从多角度对方程dy/dx-y/x=In x 求解,发现其解形式的不唯一性,而这些解只有在特殊情况下才能是真正意义上的通解.从而说明方程dy/dx+p(x)y=Q(x)的通解形式不严谨.
|
| 关 键 词： | 微分方程 通解 常数变易法 |
Questioning on the general solution to a differential equation |
| |
| WANG Wei-gang. Questioning on the general solution to a differential equation[J]. Journal of Science of Teachers＇College and University, 2011, 31(2): 54-55. DOI: 10.3969/j.issn.1007-9831.2011.02.016 |
| |
| Authors: | WANG Wei-gang |
| |
| Affiliation: | WANG Wei-gang(Department of Science and Technology,Tongcheng Teachers College,Tongcheng 231402,China) |
| |
| Abstract: | It was found that the solution to the differential equation dy/dx-y/x=lnx is not unique if solved from multi-angles by means of constant variation method,but only in exceptional circumstances all these solutions are really general solutions.The example shows that the general solution to the differential equation dy/dx+p(x)y=Q(x) is not rigorous. |
| |
| Keywords: | differential equation general solution constant variation method |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
