微分方程积分因子的求法
关键词 积分因子;全微分方程;观察;公式;分组
The Solution about First Order Differential Equation
of Intergral Factor
Abstract：At present about first order differential equations solving method of integral factor is introduced, the comparison scattered in general mostly confined to a textbook，such as formula method usually gives a factor of or contains points of functions of one variable, rarely involved the binary case, the integral factor for France have not outlined a system, so integrating factor for France has broad research space. first order ordinary integral equation flexible, perse types of equations, which can be different for the equation type of research to adapt their methods to solve the paper will be based on the definition and nature of the integrating factor through different classification methods, based on the existing method of integrating factor, the method for finding a variety of deepening and expanding comprehensively summed Some of the more regular solution: observation, formula method and grouping method, given conditions of use of these methods, and methods were to prove the feasibility of combining specific issues discussed by the three methods of research, solving Some first-order problem solving is often integral equations.
Key words:Integral factor；observation；formula；grouping
目 录
摘 要 1
1引言 2
2几种简单的一阶微分方程的积分因子的求法 3
2.1观察法 3
2.2公式法 12
3较为复杂的一阶微分方程积分因子的求法 19
3.1分组法 19
4一阶微分方程求法的综合应用 21
5结束语 22
参考文献 23
致谢 24
微分方程积分因子的求法
引言
常微分方程是数学应用联系实际的主要方法之一.他的主要的研究的问题是对常微分方程的求解在常微分方程的理论中,一般把一阶常微分方程认为是微分方程的基本，在常微分中据有十分重要的地位，一阶常微分方程初等解法主要有两种:一种是找出方程的积分因子,将方程化为全微分方程进行求解，另一种便是用变量代换法,将方程化成变量分离型方程求解.这类通过积分因子将方程化为全微分方程进行求解的方法既灵活又难以掌握,因此对积分因子的求法进行系统的研究很有必要而且意义非常重要.微分方程在技术科学和自然科学领域中都有着广泛的应用.
同样,在社会科学的某些领域里也有关于微分方程的问题.这些问题都有可能会涉及到一阶微分方程的求解,因此就会涉及到一阶微分方程的积分因子的求法，所以,对一阶微分方程积分因子的求解方法进行研究对诸多领域所涉及到一阶微分方程的求解将有很大帮助.这样做能够大大缩小求解一阶微分方程通解的计算量，能更加快捷地处理问题，因此研究微分方程积分因子的求法有着重要的现实意义和实际应用价值.
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