毕业论文----常微分方程积分因子法的求解

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1、 I 摘摘 要要 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，

2、 这就需要用到这里我 们讨论的积分因子了。 关键词：微分方程；积分因子；恰当微分方程；一阶微分； II 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 p

3、eople 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 oft

4、en 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 t