| 一类特殊的一阶常微分方程的初等积分法 |
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| 引用本文： | 刘颖. 一类特殊的一阶常微分方程的初等积分法[J]. 沈阳航空工业学院学报, 2004, 21(5): 90-91 |
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| 作者姓名： | 刘颖 |
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| 作者单位： | 沈阳航空工业学院理学系,辽宁,沈阳,110034 |
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| 摘 要： | 微分方程是与微积分同时诞生的，从诞生的时候起，人们就试图用初等积分法求微分方程的解。经过一百多年的努力，人们掌握了一些可以用初等积分法求解的微分方程类型，也发现有许多微分方程无法用初等积分法求解。但还有很多微分方程可用初等积分法求解，只是人们还没有发现它们。所以，用初等积分法求解微分方程仍是微分方程领域的一个基本研究内容。在这篇文章里讨论了一类类似黎卡提方程的一阶微分方程的初等积分法。
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| 关 键 词： | 初等积分法 常微分方程 通解 |
| 文章编号： | 1007-1385(2004)05-0090-02 |
| 修稿时间： | 2004-07-13 |
Elementary integration method for A kind of differential equation |
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| LIU Ying. Elementary integration method for A kind of differential equation[J]. Journal of Shenyang Institute of Aeronautical Engineering, 2004, 21(5): 90-91 |
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| Authors: | LIU Ying |
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| Abstract: | Differential equation was produced at the same time infinitesimal calculus emerged and they were people tried to use elementary integration to acquire the solutions of differential equation.Over 100 years effort makes people grasp some types of differential equations which will be solved using elementary integration and also discover many types of differential equations which can not be solved using elementary integration.However ,there exist a large number of differential equations which can be solved by using elementary integration,but have wat been discovered.Therefore,to solve differential equation using elementary integration is still basic research of differential equation.This article makes several elementary integration examples of one kind of differential equation which is similar to Riccati equations. |
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| Keywords: | elementary integration differential equation general solution |
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