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微分因子 [wēi fēn yīn zǐ]
differential divisor
- 摘要本文推广了一阶微分方程复合型积分因子的概点，给出了复合型积分因子的存在定理和计算公式，所得结果涵盖并推广了相关文献的结论。
This article gives a new definition of complex integrating factor about first order ordinary differential equation and a new existence theorem of a type of integral factor and calculation formual, and the resuct in this paper amplifies the conclusions in the relevant reference. - 采用积分因子方法将一阶微分方程转化为全微分方程是求解微分方程一个重要手段,讨论了积分因子存在的充要条件及确定若干特殊类型积分因子的准则;通过实例来说明准则的应用方法。
Transforming first order differential equation to complete differential equation by the way of integrating factors is an important means to seek solution for differential equations.This paper discusses the sufficient and necessary condition for existence of integrating factors and rules of determining some special kinds of integrating factors.It also takes some actual examples to explain the application of rules. - 积分因子方法是求解常微分方程的一种常用的方法.但目前常微分方程的教材中仅讨论了一些非常简单的积分因子的求解方法.介绍两种形式的积分因子的存在条件及其一些应用,这两种积分因子不但可适用于更一般的常微分方程,而且也使教材已求解的积分因子成为本文的特例.
In the problem of solving ordinary differential equation,using integrating factor is a useful method.But texts in ordinary differential equation only give some so simple equation that it can be solved by using integrating factor.This article will give two types of integrating factor:u(x~αy~β),u(ax~m+by~n),obtain the existence conditions,and apply these results for solving more complicated ordinary equation whose results are more general than those in the texts.
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