积分因子的一种直接求解方法  

A Direct Method for Solving Integrating Factors

作　　者：韩伟栋 沈建和 HAN Wei-dong;SHEN Jian-he(College of Mathematics and Informatics,Fujian Normal University,Fuzhou 350007,China)

机构地区：[1]福建师范大学数学与信息学院,福州350007

出　　处：《大学数学》2021年第2期58-63,共6页College Mathematics

基　　金：国家自然科学基金面上项目(11771082);福建省高校新世纪优秀人才支持计划资助项目。

摘　　要：充分利用变量分离微分方程为恰当方程的事实,通过引入有限次的变量替换并借助求导的链式法则,本文提出了一种求解积分因子的直接方法.该法针对一阶常微分方程,只要其通过有限次变量替换能化为变量分离微分方程,那么积分因子和通积分均可直接求得.By utilizing finite transformations and the chain rule of derivatives,and fully using the fact that an equation of separable variables is an integratable equation,we give a direct method for solving integrating factors.This method aims for general first-order ordinary differential equations,where the integrating factors as well as the associated first integrals can both be obtained provided the equation can be changed to a equation of separable variables by the finite transformations.

关 键 词：变量分离方程 积分因子 求解方法 

分 类 号：O175.5[理学—数学]