一阶常微分方程的解法.docx

一阶常微分方程的解法
[摘要]微分方程是研究自然科学和社会科学中的事物、物体和现象运动、,是解决其他问题的重要环节.
本文总体分为两个环节:第一部分介绍了一阶显式微分方程的多种解法,深入讨论了可分离变量的方程,可化为变量可分离方程的齐次方程,一阶线性微分方程,恰当方程,积分因子法这些特殊类型.
本文的另一部分介绍了一阶隐式微分方程的多种结合,结合可解出y,结合可解出x,不显含y的隐式方程,不显含x的隐式方程这四类特殊的情况进行探讨.
文章的最后一部分则是选取了一阶微分方程的四类非常特殊的微分方程,给出了各种通解.
[关键词]显式微分方程,可分离变量,一阶线性微分方程,齐次方程,隐式微分方程
The Method for First-order Differential Equations
Student: Wu Tao , School of Information and Mathematics
Tutor: Wu Haitao , School of Information and Mathematics
[Abstract] Differential equations is the most basic mathematical theory and methods to study the natural sciences and the social sciences things, objects and phenomena movement, evolution and variation. The first order differential equations as a basis for the problem, and is an important part of solving other problems.
This paper is divided into two areas overall:The first part introduces many kinds of solutions of differential equations of first-order explicit, it discusses the Variable separable equation in depth, The homogeneous equation can be separated equations for variables, First order linear differential equations, The appropriate equations ,Integral factor method,and so on.
Another part of the article describes bination of a variety of first-order differential equations implicit, Y can be solved in conjunction, X can be solved in conjunction, The implicit equation without Y, The implicit equation without X, These four kinds of special cases are discussed in this paper.
The last part of the article is selected four kinds of differential equations of first order differential equation is very special, It gives the general solution.
[Keywords] Explicit differential equation, Separable variables, First order linear differential equations, Homogeneous equation, Implicit differential equation.
一阶常微分方程的解法
前言
微分方程差不多是和微积分同时先后产生的,苏格兰数学家耐普尔创立对数的时候,,、法国数学家克雷洛、达朗贝尔、拉格朗日等人又不断地研究和丰富了微分方程的理论. 
常微分方程的形成与发展是和力学、天文学、物理