| 用二次常数变易法解几类非线性微分方程 |
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| 引用本文： | 农丽娟,王五生.用二次常数变易法解几类非线性微分方程[J].河池师专学报,2008(5):29-32. |
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| 作者姓名： | 农丽娟 王五生 |
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| 作者单位： | 河池学院数学系,广西宜州546300 |
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| 基金项目： | 1、广西新世纪教改工程“十一五”第三批资助项目（桂高教[2007]109号）;2、广西教育厅科学研究资助项目（编号：200707MS112）;3、河池学院应用数学重点学科资助项目（院科研[2007]2号）;4、河学院重点课程资助项目（院教学[2008]9号）. |
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| 摘 要： | 非线性微分方程没有一般的求解方法，而常数变易法是求解一阶线性微分方程的主要方法．文献1～3]研究了解非线性微分方程的常数变易法，其中文献2]提出了用二次常数变易法求解非线性微分方程的一些具体例子．作者在此基础上构造了可用二次常数变易法求解的一阶非线性微分方程的类型，并给出相应的例子来说明二次常数变易法的重要性．
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| 关 键 词： | 一阶非线性微分方程 常数变易法 二次常数变易法 通解 |
The Method of Quadratic Constant Variation for Solving Several Kinds of Nonlinear Differential Equations |
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| NONG Li-juan,WANG Wu-sheng.The Method of Quadratic Constant Variation for Solving Several Kinds of Nonlinear Differential Equations[J].Journal of Hechi Normal College,2008(5):29-32. |
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| Authors: | NONG Li-juan WANG Wu-sheng |
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| Institution: | ( Department of Mathematics, Hechi University, Yizhou, Guangxi 546300, China) |
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| Abstract: | There are no general methods for solving nonlinear differential equation while the method of constant variation is the main method of solving first - order linear differential equation. The references 1,2,3 ] research the method of constant variation for solving nonlinear differential equation. There are some concrete examples of nonlinear differential equation which can be solved by the method of quadratic constant variation in the document 2 ]. On its basis, this paper discusses some types of first - order nonlinear differential equation which can be solved by quadratic constant variation, and makes corresponding examples to explain the importance of the method of quadratic constant variation. |
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| Keywords: | First - order nonlinear differential equation Method of constant variation Method of quadratic constant variation General solutions |
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