一阶微分方程存在特混型积分因子的新充要条件  

New Necessary and Sufficient Conditions for the Existence of Special Mixed Type Integral Factors in First Order Differential Equations

作　　者：樊豫陇 王明建 FAN Yu-Long;WANG Ming-jian(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）》2022年第1期7-9,18,共4页Journal of Xi’an University(Natural Science Edition)

基　　金：国家自然科学基金项目(11161018)。

摘　　要：利用初等方法,讨论了一阶微分方程P(x,y)dx+Q(x,y)dy=0,给出其存在特混型积分因子μ=μ(x,y)=1/xP±yQ(xP±yQ≠0)的一个新充要条件,借助齐次函数的性质和偏微分法等给以证明,且说明结论与文[1]并不等价,最后给出具体应用举例.In this paper,the first-order differential equation P(x,y)dx+Q(x,y)dy=0 is discussed by using the elementary method,and a new necessary and sufficient condition for its existence of special mixed integral factor μ=μ(x,y)=1/xP±yQ(xP±yQ≠0) is given.It is proved by means of the properties of homogeneous function and partial differential method,and it is shown that the conclusion is not equivalent to that in the text[1].Finally,a specific application example is given.

关 键 词：微分方程 积分因子 充要条件 齐次函数 应用 

分 类 号：O175.1[理学—数学]