一阶常微分方程初等解法.doc毕设论文.doc

目 录 摘 要…………………………………………………………………………………......1 关键词………………………………………...…………………………………………...1 Abstract…………………………………………………………...………………………1 Keywords………………………………………………………………………..………..1 0 前 言…………………..……………………………………………………………...1 1 预备知识………………………………………………………………………..……...1 1. 1变量分离方程……………………………………………………………………….2 1. 2恰当微分方程……………………………………………………………………….2 1. 3积分因子………………………………………………………………….…………2 2 基本方法……………………………………………………………??…………..…...2 2. 1一般变量分离……………………………………………………………………….3 2. 2齐次微分方程……………………………………………………………………….3 2. 2 .1齐次微分方程类型一………………………………………………………….3 2. 2. 2齐次微分方程类型二……………………..……...……………………………4 2. 3常数变易法…………………………..………………...……………………………5 2.3.1常数变易法一…………………………….……………………………………5 2.3.2常数变易法二……………………….…………………………..……………..6 2.4积分因子求解法…………………………………..…………………………………7 2.5恰当微分方程求解法…………………………………………..……………………8 3 基本方法的应用……………………………………………..………………………8 3. 1一般变量分离方程应用…………………………………………….………………8 3.1.1应用举例……………………………………………………….………………9 3.1.2应用举例………………………………………...……..………………………9 3. 2齐次微分方程应用……………………………………...…………………………10 3.2.1类型一应用举例…………………………………...…………………………10 3.2.2类型一应用举例………………………………………………………………11 3.2.3类型二应用举例………………………………………………………………11 3.2.4类型二应用举例………………………………………...……………………12 3.3常数变易法应用……………………………………………………………………13 3.3.1常数变易法应用举例……………………………………..…….……………13 3.3.2伯努利微分方程应用举例………………………………………...…………14 3. 4利用积分因子求解……………………..……………………...……..……………14 3. 5 利用恰当微分方程求解……………………………………………....……..……15参考文献……………………………...………………..…………………......…………16 一阶常微分方程初等解法 摘 要: 本文对一阶微分方程的初等解法进行归纳与总结,同时简要分析了变量分离,积分因子,恰当微分方程等各类初等解法.并且结合例题演示了如何把常微分方程的求解问题化为积分问题,进行求解. 关键词: 一阶常微分方程;变量分离;恰当微分方程;积分因子 The Fundamental methods of the first-order ordinary differential equation Abstract: In this thesis, we summarize the fundamental methods of the first-order ordinary differential equation. At the same time, we analysis the various types of fundamental methods such as the separation of variables, integrating factor and the exact differential equation. Combined with examples, we show how the ordinary differential equations