三类复合型积分因子的充分必要条件及其应用 |
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引用本文: | 陈星海,李璜,韩祥临.三类复合型积分因子的充分必要条件及其应用[J].湖州师专学报,2010(2):44-49. |
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作者姓名: | 陈星海 李璜 韩祥临 |
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作者单位: | [1]湖州师范学院理学院,浙江湖州313000 [2]杭州电子科技大学理学院,浙江杭州310000 |
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基金项目: | 浙江省新世纪教革项目(ZC09063);湖州师范学院重点教改项目(GJB09004);湖州师范学院微分方程精品课程. |
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摘 要: | 利用μ(x,y)是一阶微分方程积分因子的充要条件,讨论了一阶微分方程的积分因子问题,给出三个不同类型的复合型积分因子μp(x)+f(x)g(y)+q(y)],μφ(xsyt)+p(x)+q(y)],μφ(xsyt)+p(x)q(y)]存在的充分必要条件及相应的推论,并结合实例给出具有上述形式积分因子的求解方法.
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关 键 词: | 一阶常微分方程 复合型积分因子 充分必要条件 应用 |
The Necessary and Sufficient Conditions of the Three Complex Integrating Factors and Their Application |
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Institution: | CHEN Xing - hai, LI Huang , HAN Xiang - lin ( 1. Faculty of Science, Huzhou Teachers College, Huzhou 313000, China ; School of Science, Hangzhou Dianzi University of Science & Technology, Hangzhou 310000, China) |
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Abstract: | Using the necessary and sufficient condition of μ(x,y) for the first order ordinary differential equations, this paper discusses the problem of integral factors and gives the property of existence of the necessary and sufficient conditions and their corresponding inference for the three different composite- type integral factorsμp(x)+f(x)g(y)+q(y)],μφ(xsyt)+p(x)+q(y)],μφ(xsyt)+p(x)q(y)] and the solving method with practical examples. |
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Keywords: | first order ordinary differential equations complex integrating factor necessary and suffi cient condition application |
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