| 论二阶齐线性方程的两个不变量 |
| |
| 引用本文： | 蔡鑫,黄健吾.论二阶齐线性方程的两个不变量[J].闽江学院学报,2005,25(2):25-30. |
| |
| 作者姓名： | 蔡鑫 黄健吾 |
| |
| 作者单位： | 闽江学院数学系,福建,福州,350108 |
| |
| 摘 要： | 讨论了形如x^n P(t)x′ q(t)x=0的二阶齐线性方程，推广了文1]中该方程两个不变量I(t)△↑-q(t)-1/4q^2(t)-1/2p′（t）和J（t）△↑-q′（t） 2p(t)q(t)/1|q(t)|3/2的证明，并由此推出几类齐线性方程可化为常系数方程或易求解的方程的情形及它的通解，推广了文2]的4种情形。
|
| 关 键 词： | 二阶齐线性方程 不变量 常系数方程 通解 |
| 文章编号： | 1009-7821(2005)02-025-06 |
| 修稿时间： | 2005年2月1日 |
The Two Invariants of Homogeneous Linear Differential Equations of Order Two |
| |
| CAI Xin,UANG Jian-wu.The Two Invariants of Homogeneous Linear Differential Equations of Order Two[J].Journal of Minjiang University,2005,25(2):25-30. |
| |
| Authors: | CAI Xin UANG Jian-wu |
| |
| Abstract: | The paper discusses homogeneous linear differential equations of order two about xn+P(t)x'+q (t)x=0. It extends the proof of the two invariants in paper 2] which are I(t) (?)q(t)-1/42(t)-1/2p'(t) and J(t) (?) 2|q(t)|3/2/q'(t)+2q(t)q(t), and pullouts some homogeneous linear differential equations, which can be changed into constant coefficient equations or others solved easily, and ordinary solutions. Furthermore, this paper provides four conditions based on the conclusion in 2]. |
| |
| Keywords: | homogeneous linear differential equations of order two invariant constant coefficient equadon ordinary solution |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
