| 一类一阶微分方程初等解法的分析研究 |
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| 引用本文： | 白福梅.一类一阶微分方程初等解法的分析研究[J].山西农业大学学报(自然科学版),2012,32(5). |
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| 作者姓名： | 白福梅 |
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| 作者单位： | 晋中师范高等专科学校,山西晋中,030600 |
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| 摘 要： | 对一阶微分方程变量分离方程dy/dx=f(x)φ(y)(其中f(x),φ(y)分别是x,y的连续函数)和非齐次线性微分方程dy/dx=p(x)y+Q(x)(其中p(x),Q(y)是x的连续函数)的其初等解法进行了分析研究,结合Lebesgue积分与Riemann积分的相关知识,给出了f(x),φ(y),p(x),Q(x)的不连续点集是零测集时的初等解法。
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| 关 键 词： | 一阶微分方程 变量分离方程 非齐次线性微分方程 零测集 |
Elementary Solution to a Kind of First-Order Differential Equation |
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| Bai Fumei.Elementary Solution to a Kind of First-Order Differential Equation[J].Journal of Shanxi Agricultural University,2012,32(5). |
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| Authors: | Bai Fumei |
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| Abstract: | For the separation of variable equation dy/dx=f(x)φ(y),where f(x),φ(y) are continuous function of "x,y",as well as non-homogeneous linear differential equations of first-order differential equations dy/dx=p(x)y+Q(x),where p(x),Q(y) is continuous function of x.In this paper,the elementary solution was analyzed,combined with Lebesgue integral and Riemann integral related knowledge,the elementary solution was given when the discrete point set was zero test set. |
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| Keywords: | First order differential equations Variable separation equations Non-homogeneous linear differential equations Zero measurable set |
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