关于克莱罗方程的奇解与包络概念之拓展  

Extension of the Singular Solution for Clairaut Equation

作　　者：刘姗姗 韩茂安[1] LIU Shan-shan;HAN Mao-an(College of Mathematics and Science,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《大学数学》2018年第3期17-25,共9页College Mathematics

摘　　要：如所周知,克莱罗方程y=xy′+f(y′)有一个特解,在f″(y′)≠0条件下该特解就是一个奇解,并对应一个包络.本文假设这一条件不成立,在其他一些条件之下讨论特解的性质,我们特别给出了广义包络的概念,并研究其存在条件.It is well known that Clairaut equationy=xy′＋f（y′）has a particular solution.The particular solution is a singular solution and corresponds to an envelope iff″（y′）≠0.In this article we assume that this condition fails to hold and discuss the properties of particular solution under some other conditions.In particular,we give the concept of generalized envelope and study the existence conditions.

关 键 词：克莱罗方程 奇解 特解 广义包络 

分 类 号：O175.1[理学—数学]