| Riccati方程的可积条件 |
| |
| 引用本文： | 钱明忠,陈友朋.Riccati方程的可积条件[J].洛阳师范学院学报,2005,24(2):24-26. |
| |
| 作者姓名： | 钱明忠 陈友朋 |
| |
| 作者单位： | 盐城师范学院数学系,江苏,盐城,224002 |
| |
| 摘 要： | 黎卡提(Riccati)方程y′=p(x)y2+q(x)y+r(x)一般情况下是不可积的,本文利用变量变换先将Riccati方程化成二阶变系数齐线性方程,再化成二阶常系数线性方程.从而得到Riccati方程的若干可积条件.
|
| 关 键 词： | Riccati方程 二阶常系数齐线性方程 变量变换 |
| 文章编号： | 1009-4970(2005)02-0024-03 |
| 修稿时间： | 2004年10月18 |
Integrable Conditions on Riccati Equation |
| |
| QIAN Ming-zhong,CHEN You-peng.Integrable Conditions on Riccati Equation[J].Journal of Luoyang Teachers College,2005,24(2):24-26. |
| |
| Authors: | QIAN Ming-zhong CHEN You-peng |
| |
| Abstract: | Riccati equation y’=p(x)y_2+q(x)y+r(x) had no elementary solution in general case. In this paper, we first transfer the Riccati equation to second order linear homogenous equation with variable coefficients by variable transformation, and use the variable transformation to transfer the obtained second order linear homogeneous equation with variable coefficients to second order linear homogeneous equation with constant coefficients, then we obtain some integrable conditions on Riccati equation. |
| |
| Keywords: | Riccati equation second order linear homogeneous equation with constant coefficients variable transformation |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
