﻿ 微分方程中包络的定义及求奇解时必须注意的一个问题 Definition of Envelope in Differential Equations and a Problem that Must Be Noticed When Seeking Singular Solution

Pure Mathematics
Vol.07 No.04(2017), Article ID:21298,6 pages
10.12677/PM.2017.74035

Definition of Envelope in Differential Equations and a Problem that Must Be Noticed When Seeking Singular Solution

Zhihong Kong

Department of Mathematics, Taiyuan Normal University, Jinzhong Shanxi

Received: Jun. 18th, 2017; accepted: Jul. 3rd, 2017; published: Jul. 10th, 2017

ABSTRACT

In this paper, we explain that why the definition of envelope in differential equations is different from differential geometry, and give examples to illustrate. In addition, we illustrate a problem that must be noticed when seeking singular solution.

Keywords:Envelope, Tangent, Singular Solution, Supplement Function Value

1. 包络的定义问题

, (1)

2. 举例说明

(2)

,

,

.

(3)

, (4)

。c—判别式为

(5)

,

.

(6)

(7)

(8)

,

,.

3. 求奇解时必须注意的一个问题

(9)

,

, (10)

,

.

(11)

,

, (12)

。已知是方程的解，而在通解中当，补充定义；同理，补充定义，解方程组(c—判别式)

(或)时，通解(12)，其中，就表示了方程所有的解，接下来可以直接

Definition of Envelope in Differential Equations and a Problem that Must Be Noticed When Seeking Singular Solution[J]. 理论数学, 2017, 07(04): 271-276. http://dx.doi.org/10.12677/PM.2017.74035

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