| 二阶常系数微分方程解法的简化 |
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| 引用本文： | 熊灿,谢建新.二阶常系数微分方程解法的简化[J].南昌水专学报,2010,29(1):5-8. |
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| 作者姓名： | 熊灿 谢建新 |
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| 作者单位： | [1]湖南电子科技职业学院基础课部,湖南长沙410217 [2]长沙理工大学数学与计算机科学学院,湖南长沙410006 |
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| 摘 要： | 给出了二阶常系数齐次线性微分方程通解的三角函数形式或双曲函数形式，同时得出了利用位移定理。结合待定系数法解几类特殊的二阶常系数非齐次线性微分方程的方法，简化了此类微分方程的求解过程．
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| 关 键 词： | 二阶常系数微分方程 Leibniz定理 位移定理 解法 |
Simplification of solution of differential equation with second-order constant coefficients |
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| XIONG Can,XIE Jian-xin.Simplification of solution of differential equation with second-order constant coefficients[J].Journal of Nanchang College of Water Conservancy and Hydroelectric Power,2010,29(1):5-8. |
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| Authors: | XIONG Can XIE Jian-xin |
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| Affiliation: | 1.Department of Basic Courses/a>;Hunan Electronic Science and Technology Institute/a>;Changsha 410217/a>;China/a>;2.College of Mathematics and Computer Science/a>;Changsha University of Science and Technology/a>;Changsha 410006/a>;China |
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| Abstract: | We presented the trigonometric function or hyperbolic function of the general solution of the homogeneous linear differential equation with constant coefficient in the paper.Meanwhile,we obtained the method to solve some special nonhomogeneous linear differential equation with second-order constant coefficients by combining undetermined coefficient method and the displacement theorem,which simplified the solution process of this kind of differential equation. |
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| Keywords: | differential equation with second-order constant coefficient Leibniz theorem displacement theorem solution simplification |
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