二阶线性齐次微分方程的一个可积定理  

An Integrable Theorem of Second Order Linear Homogeneous Differential Equation

作　　者：张学元[1] 

机构地区：[1]湖南工程学院数理系,湖南湘潭411104

出　　处：《上海第二工业大学学报》2002年第1期14-19,共6页Journal of Shanghai Polytechnic University

摘　　要：对二阶线性齐次微分方程引入预解方程和预解常数的概念,运用双变换棗未知函数变换和自变量变换方法得到了一个新的实用的可积充分条件,推广了经典的和近代的可积性结果,扩大了常微分方程封闭求积的范围。Two concepts of resolvent constant and resolvent equation are introduced for the two-order linear homogeneous differential equation, and a new practical integrable sufficient condition is derived and some classical and modern integrable results are extended. Thus the closed solvable range of ordinary differential equation was extended.

关 键 词：可积定理 二阶线性齐次微分方程 预解方程 预解常数 通解 未知函数变换 自变量变换 可积定理 

分 类 号：O175.1[理学—数学] R241.81[理学—基础数学]