摘要
提出了一类新二阶变系数线性微分方程,说明这类方程一般是没有初等解的.然后对这类方程引进特征方程,给出了一个实用的可积充分判据及其通解的积分表达式,从而扩大了常微分方程的封闭可解范围.
In this paper given was kind of second order diferential equation with variable coefficient , through they are not elementary solutiona in ordinary condition. And then, the concept of the charaeteristic equation is introduced, a practical integral sufficient criterion and the integral expression formula of it's general solution for this kind equation are given. Some classical and modem solvable results are extended, and endosed-integration region of ordinary differential equation is extended.
出处
《邵阳学院学报（自然科学版）》
2005年第1期2-4,共3页
Journal of Shaoyang University：Natural Science Edition
关键词
新二阶变系数线性非齐次微分方程
特征方程
可积判据
通解的积分表达式
second order linear non-homogeneous differential equation with variable coefficient
characteritic equation
itegral criterion
integral expression of the general solution
