| 一类一阶微分方程与Riccati方程的等价关系 |
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| 引用本文： | 王明建,王五生,石东洋.一类一阶微分方程与Riccati方程的等价关系[J].河南科学,2014(4):479-481. |
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| 作者姓名： | 王明建 王五生 石东洋 |
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| 作者单位： | [1]郑州师范学院数学与统计学院,郑州450044 [2]广西河池学院数学系,广西河池546300 [3]郑州大学理学院,郑州450052 |
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| 基金项目： | 基金项目：河南省教育厅“十二五”规划项目[2011]-JKGHAD-0309 |
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| 摘 要： | 证明了一类一阶常微分方程dy/dx=g′/gy+qΦ(ay+f)G(g)]-f′/a+fg′/ag+αq(其中a,b和α都是实常数,f=f(x),g=g(x)和u=u(x)都是x的连续可微函数,Φ(u)是u的连续函数,G(g)是g的连续函数,且G(g)≠0))与Riccati方程在某些条件下的等价性,同时给出了与文献1]不同的解法.
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| 关 键 词： | 常微分方程 Riccati方程 等价性 |
Equivalent of a Class of First Order Differential Equation and Riccati Equation |
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| Wang Mingjian,Wang Wusheng,Shi Dongyang.Equivalent of a Class of First Order Differential Equation and Riccati Equation[J].Henan Science,2014(4):479-481. |
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| Authors: | Wang Mingjian Wang Wusheng Shi Dongyang |
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| Institution: | 1. College of Mathematics and Statics, Zhengzhou Normal University, Zhengzhou 450044, China; 2. Department of Mathematics, Hechi University, Hechi 546300, Guangxi China; 3. Department of Mathematics and Statics, Zhengzhou University, Zhengzhou 450052, China) |
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| Abstract: | Equivalent of a class of first order differential equation dy/dx =g′g y＋qΦ（a y＋f）G（g）]-f′/a ＋fg′/ag ＋αq （there a,b and α are real constant, f,g and u are continuous and differentiable function,Φ（u） and G（g） are continuous function,and G（g）≠0） and Riccati equation is given,and the some error in articles1] are correcting. |
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| Keywords: | order differential equation Riccati equation equivalent |
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