摘要 常微分方程，是数学相关的专业中的一门很重要的基本课，是相关的课程中的很 重要的一个构成。常微分方程将抽象的没有实体的数学理论和自然科学的实际运用联 系了起来，微分方程的理论是许多理论分析问题的想法以及不同现实实用的方法的结 合，这中间的对微分方程进行求解还有对所求解的性质的研究长久以来都是相关学者 的一个很重要的根本的工作。但是实际应用以及科学研究中绝大多数的微分方程无法 得到通解，因为这些方程过于复杂，学者们只能用数值方法来计算出常微分方程的近 似的解。 78068

状态空间法是一种基于解答空间的问题表示和求解方法，具有很多优点，因为它 降低了方程的阶次，有利于之后的计算求解。 

本文的主要任务就是基于对状态空间法的运用，将一般的微分方程进行转化，进 而得到一组新的微分方程组，从而得到一个关于向量的一阶偏微分方程。 

这这篇论文中，我们首先对常微分方程组的部分基本概念进行了回顾，介绍了求 一阶齐次微分方程组，非齐次微分方程组基解的方法和步骤，接着介绍了状态空间法 的基本概念、理论以及适用情况，总结状态空间法的各种求法，同时给出了状态空间 法在实际中的一些应用。

毕业论文关键词：常微分方程；状态空间法；微分方程组 

Abstract Often differential equation is a very important basic course of the mathematical disciplines。 It is an important part of the curriculum system, as the connection of the main bridge of abstract mathematical theory and natural science applications, its development promoted the linear algebra, Lie group theory, control theory and so on a series of disciplines, such as a study。 The theory of differential equations has been combined with many kinds of theories and methods。 The solution of the differential equations and the properties of the solutions have always been an important basic work of the researchers。 However, most of the ordinary differential equations which are encountered in the actual production and scientific research because of they are complexity, basically, we can not get the analytical solution, so the numerical method is usually used to find the approximate solution。。

State-space method is a solution of problem representation and solution method。 It’s based on solution space。 State-space method has many advantages, because it reduces the order of the equation。 It is beneficial to solve the problem。

The main task of this paper is based on the use of state space method, the general differential equations are transformed and a new set of differential equations, so as to obtain a vector of first-order partial differential equations。

In this paper, we first review the basic concepts of ordinary differential equations, for first order homogeneous differential equations, non-homogeneous differential equations based solution methods and steps, then introduces the state space method of the basic concept, theory and application, summarize the state space method of variety seeking method, and gives the state space method in practical application。

Keywords: ordinary differential equation; state space method; differential equation

目      录 

第一章  绪论-1 

1。1 前言1 

1。2 本文的主要工作--4 

第二章  常微分方程--5 

2。1 常微分方程的基本概念--6 

2。2 求解常微分方程组7 

2。2。1 线性常系数齐次性微分方程组的求解7 

2。2。2 线性常系数非齐次性微分方程组的求解-8 

2。3 小结--10