一阶微分方程存在混合特型积分因子充要条件初探  

Preliminary Research on A Sufficient and Necessary Condition for the Existence of Mixed Characteristic Integral Factor in First Order Differential Equation

作　　者：王明建 赵路 WANG Ming-jian;ZHAO Lu(Department of Basic Education, Huanghe Jiaotong University, Jiaozuo 454950, China)

机构地区：[1]黄河交通学院基础教学部,河南焦作454950

出　　处：《西安文理学院学报（自然科学版）》2021年第1期14-16,共3页Journal of Xi’an University(Natural Science Edition)

基　　金：国家自然科学基金项目(11161018)。

摘　　要：针对一阶微分方程P(x,y)dx+Q(x,y)dy=0,探讨了该方程存在混合特型积分因子μ=μ(x,y)=1xP±yQ(xP±yQ≠0)的充要条件,并利用微分法和偏微分方程解的性质加以证明,同时给出具体的应用举例.For the first order differential equation P(x,y)dx+Q(x,y)dy=0,the necessary and sufficient conditions for the existence of mixed special integral factorsμ=μ(x,y)=(xP±yQ≠0)are discussed.It is proved by using the differential method and the properties of solutions of partial differential equations,and the concrete application examples are given.

关 键 词：微分方程 积分因子 充要条件 应用 

分 类 号：O175.1[理学—数学]