一阶常微分方程有形如μ(ax~α+bx^sy^l+cy~β)积分因子的充要条件  

A Sufficient and Necessary Condition of Integral Factor Such As μ(ax~α+bx^sy^l+cy~β) for First Order Ordinary Differential Equation

作　　者：陈明玉[1] 

机构地区：[1]泉州师范学院数学系,福建泉州362000

出　　处：《大学数学》2005年第1期130-133,共4页College Mathematics

基　　金：泉州师范学院专款资助科研项目(2002 I 08)

摘　　要：讨论了一阶常微分方程M(x,y)dx+N(x,y)dy=0 的积分因子问题,给出了一阶常微分方程有形如μ(axα+bxsyl+cyβ)的积分因子的一个充分必要条件.推广了相关文献的结果,从而丰富了常微分方程的解法.This paper discusses the problem of integral factor about the first order constant differential equation: (M(x,y)dx+N(x,y)dy)=0, gives a sufficient and necessary condition of integral factor such as μ(ax~α+bx^sy^l+cy~β) for first order ordinary differential equation, and makes an extension form the conclusion of related reference. The results in this paper perfect the method of solving ordinary differential equation.

关 键 词：一阶常微分方程 积分因子 可微函数 充分必要条件 

分 类 号：O175.1[理学—数学]