常微分方程的初等解法与求解技巧

常微分方程的初等解法与求解技巧

山西师范大学本科毕业论文（设计）

常微分方程的初等解法与求解技巧

姓 名 院 系 专 业 班 级 学 号 指导教师 答辩日期 成 绩

张娟

数学与计算机科学学院

信息与计算科学

1251020126 王晓锋

1 / 26

常微分方程的初等解法与求解技巧

常微分方程的初等解法与求解技巧

内容摘要

常微分方程在数学中发挥着举足轻重的作用，同时它的应用在日常生活里随处可见，因此掌握常微分方程的初等解法与求解技巧是非常必要的.本论文主要论述了其发展、初等解法与求解技巧，前者主要有变量分离、积分因子、一阶隐式微分方程的参数表示，通过举例从中总结出其求解技巧，目的是掌握其求解技巧.

【关键词】变量分离 一阶隐式微分方程 积分因子 求解技巧

2 / 26

常微分方程的初等解法与求解技巧

Elementary Solution and Solving Skills of Ordinary

Differential Equation

Abstract

Ordinary differential equations take up significant position in mathematics, and at the same time, the application of it can be seen everywhere in our daily life, therefore, it’s necessary to grasp the elementary solution of ordinary differential equations and solving skills. This paper mainly introduced the definition of ordinary differential equations, elementary solution method and solving skills, the former mainly included the separation of variables, integral factor, a parameter-order differential equations implicit representation, by way of examples to sum up their solving skills, the purpose is to master the skills to solve.

【Key Words】the separation of variables the first order implicit differential equation

integrating factor solution techniques

3 / 26