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.
作者
刘姗姗
韩茂安
LIU Shan-shan;HAN Mao-an(College of Mathematics and Science,Shanghai Normal University,Shanghai 200234,China)
出处
《大学数学》
2018年第3期17-25,共9页
College Mathematics
关键词
克莱罗方程
奇解
特解
广义包络
Clairaut equation
singular solution
particular solution
generalized envelope
