文档介绍：安徽建筑大学
毕业设计(论文)
专业信息与计算科学
班级信息一班
学生姓名刘小欢
学号 **********
课题二阶线性微分方程求解方法
指导教师张素平
2014年3月31日
摘要
二阶线性微分方程在微分理论中占有重要位置,在科学研究、工程技术中有着广泛的应用,其中有很多应用类型的问题中都归结为二阶线性微分方程的求解问题,,至今还没有一个普遍有效的方法,通常采用的级数解法只能得到某点领域内的局域解或者近似解,.
在微分方程理论中,一些特殊的微分方程的性质和解法也已经有了深入的研究,.
如果通过某些适当的变换将给定的二阶变系数微分方程化为常系数微分方程,,以及通过什么样的变换才能化为常系数微分方程.
本文通过对微分方程理论的研究,用不同的方法探讨这类问题,扩展了变系数线性微分方程的可积类型,借助变量代换等方法将给定的变系数微分方程化为常系数微分方程求解,提出二阶变系数微分方程的求解基本方法和步骤.
关键词:变系数二阶微分方程;变量代换;常数变易;通解;线性变换;
Abstract
Second order liner homogeneous differential equation play an important role in differential theories, and used extensively in science research and technology, so there have many problems with application type all turn to second order liner dirrerential equation’s solve problem. However, ordinary coefficient differential equation has solve according to liner differential equation theory. But the solve for varied coefficient second order liner differential equation is hard to get, and haven’t had thought out an efficient way to make out it so far. The most often used way is series method, which just can get its local area solve or approximate solve. It is noe appropriate to do science research and analyze. So to discuss and research the solve of varied coefficient second order liner differential equation has important applied valuable.
In differential equation theory, some special differential equation’s solve ways have already been they can be seemd as couled be solved sort of equation. But varied coefficient equation, however, the solve for this sort of equation is hard.
This article utilizes different ways to research this problem in differential equation theories, which expand the could be solved type of varied coefficient second order liner differential equation. By using variable transformation make varied coefficient second order lin