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微分方程是可以表述事物变化所遵循的基本规律的工具之一，也成为了最有生命力的数学分支。在现实生活中，许多问题都可以归结为高阶微分方程的模型，这使得探求高阶微分方程的求解是一项很有意义的工作。本文简单介绍了常微分方程的概念、发展和研究意义，主要研究了三类三阶常微分方程的求解，同时运用已有模型获得通解，最后给出理论结果加以举例应用，以加深对三阶常微分方程通解公式的理解和认识。
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Abstracts: Principle of the use of holes for a broad range, it is a mathematical combination of the most basic principle, the application of the principle holes can solve many problems concerning the existence of a combination of issues. In the 20th century, many studies are directed at holes the promotion of the principle, Ramsey theory, in which reached its peak.It is precisely because of the extensive use of pigeon holes principle, and subject to different types of answers to very different methods, so the principle of the structure of holes is also a variety of methods. In this paper, these methods have been collated and summarized to form seven commonly used construction method.
Keywords: pigeonhole principle; structure; pigeons; cage; Category
Differential equation can be expressed by things change the basic laws of one of the tools, also became the most vibrant branch of mathematics. In real life, many problems could be to blame for higher order ordinary differential equation model, this makes the search of higher order ordinary differential equation solution is a very meaningful work. This article simply introduces the concept of differential equation, the development and research significance, mainly studies three third order ordinary differential equations, and using of solving the existing model are given, finally won the general theory, for example, to deepen our application to three order ordinary differential equations of general formula of understanding and knowledge.
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