微分方程在考研数学中的应用摘要 常微分方程理论已经建立了 300 多年,它是高等数学知识体系的重要组成部分.而求解常微分方程是高等数学学习的重点,其中求解一阶、二阶微分方程是基础和重中之重.因此探究解微分方程的一般方法可以对我们高等数学学习乃至考研数学提供帮助.通过查阅图书馆文献资料、参考中国知网相关论文和近十年的考研数学真题.经过研究总结出了求解微分方程的一般方法,注意点,并且在研究的过程中发现了求解常规微分方程问题的规律和方法,由此深入研究这些规律方法及注意事项.并且根据以上的研究总结出求微分方程在考研数学中的复习建议.经研究, 在遇到问题时,首先要所判断所遇到的微分方程的题目是什么类型,需要进行怎样的变换,再则要采用什么样的办法、公式和定理等,然后针对具体问题选择合适的方法.并且微分方程求解也要求我们对相应的公式和特征方程不同的特征根的情况所对应的不同解的形式要有精确推导掌握和准确记忆.关键词 微分方程 考研数学 一般规律 复习建议The application of differential equation in mathematics of postgraduate entrance examinationAbstract The theory of ordinary differential equation has been established for more than 300 years, and it is an important part of higher mathematics knowledge system, Among them, solving first-order and second-order differential equations is the foundation and the most important. Therefore, in-depth study of special solutions and general solutions of first-order and second-order differential homogeneous and non-homogeneous equations can provide help for our higher mathematics learning and even entrance examination mathematics. Through consulting the library literature, referring to the related papers of CNKI and the real problems of entrance examination mathematics in the past ten years, this paper summarizes the research results General methods and points of attention for solving differential equations, and the laws and methods for solving ordinary differential equations are found in the process of research, so as to ...
