（毕业设计论文）《常微分方程积分因子法的求解》.docVIP

摘 要 微分方程是表达自然规律的一种自然的数学语言。它从生产实践与科学技术中产生，而又成为现代科学技术中分析问题与解决问题的一个强有力的工具。 人们在探求物质世界某些规律的过程中，一般很难完全依靠实验观测认识到该规律，反而是依照某种规律存在的联系常常容易被我们捕捉到，而这种规律用数学语言表达出来，其结果往往形成一个微分方程，而一旦求出方程的解，其规律则一目了然。 所以我们必须能够求出它的解。 同时，对于恰当微分方程我们有一个通用的求解公式。但是，就如大家都知道的那样，并不是所有的微分形式的一阶方程都是恰当微分方程。 对于这类不是恰当微分方程的一阶常微分方程该如何求出它的解呢，这就需要用到这里我们讨论的积分因子了。 关键词：； Abstract Differential expression of natural law is a natural mathematical language. It from the production practice and science and technology generation, but modern science and technology in analyzing and solving problems in a powerful tool.. Some people in the law to explore the process of the material world, the general experimental observation is difficult to completely rely on recognizing that the law, but there is a link in accordance with certain laws are often easy to catch us, and such laws expressed in mathematical language, which often results in the formation of a differential equation, and once obtained equation, the law is clear So we must be able to find its solution. Meanwhile, for the appropriate differential equation we have a general formula to solve. However, as we all know, not all forms of first-order differential equations are appropriate differential equation. For these are not appropriate differential equation differential equation, how it obtained its solution, which we are discussing here need to use the integrating factor Keywords: Differential equation; integral factor; appropriate differential equation; first-order differential 目 录 第章绪论………………………………………………………………………………………………………………………………………1 1.2 恰当微分方程……………………………………………………………………1 第章………………………………………………2 2.1 各种形式积分因子存在的充要条件……………………………………………2 2.2 几种常见类型的微分方程的积分因子…………………………………………5 第章……………………………………………7 3.1 满足条件的积分因子求法………………………………7 3.2 方程积分因子…………………………………………………………………………………………9 3.3 方程积分因子……………………………11 3.4 方程积分因子…………12 参考文献……………………………………………………………………15 致谢…………………………………………………………………………16 第章 绪论 ,但并非所有的微分方程均为恰当微分方程。如果能将一个非恰当微分方程化为恰当微分方程，则求其通解将变得简单。为此本文寻求微分方程各类积分因子,化微分方程为恰当方程求解，这