浅述积分因子与方程解的联系  

Relation Between Integral Factor and Equation Solution

作　　者：饶梦真 谭钦洋 齐静 张昕[1] RAO Mengzhen;TAN Qinyang;QI Jing;ZHANG Xin(School of Mathematics,South China Normal University,Guangzhou 510006,China;School of Mathematics and Computer Science,Foreign Trade and Business College of Chongqing Normal University,Chongqing 401520,China)

机构地区：[1]华南师范大学数学科学院,广东广州510006 [2]重庆师范大学涉外商贸学院数学与计算机学院,重庆401520

出　　处：《海南师范大学学报（自然科学版）》2020年第3期280-286,共7页Journal of Hainan Normal University（Natural Science）

摘　　要：文章简述了几类微分方程及其积分因子的形式,给出积分因子的相关性质,叙述了如何利用一个方程的两个不同的积分因子对方程进行快速求解,在此过程中引用了雅可比行列式为零的相关结论(函数相关的结论),修正了文献中的一处不足,证明了一个方程中两个积分因子之间的函数关系,最后给出了一类齐次微分方程的快速求解法。In this paper,several kinds of differential equations and the forms of their integral factors were briefly introduced,the related properties of the integral factors were mainly given,and how to use two different integral factors of an equation to solve the equation quickly was described.In this process,the related conclusion that Jacobian determinant is zero(function related conclusion)was quoted,and one of the shortcomings in reference was corrected.The functional relationship between two integral factors in an equation was proved.Finally,a fast solution of a class of homogeneous differential equation was given.

关 键 词：微分方程 积分因子 雅可比行列式 函数相关 性质 

分 类 号：O175.14[理学—数学]