| 高阶常系数线性微分方程的一种积分形式特解 |
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| 引用本文： | 刘凌. 高阶常系数线性微分方程的一种积分形式特解[J]. 高等数学研究, 2011, 14(1): 73-74 |
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| 作者姓名： | 刘凌 |
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| 作者单位： | 上海理工大学理学院,高等教学教研室,上海,200090 |
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| 摘 要： | 利用微分算子及n阶常系数非齐次线性微分方程的特征方程根与系数的关系给出其特解的逐次积分形式,并由此给出自由项f(x)=Pm(x)eλx(其中Pm(x)为m次多项式)时特解的简单递推公式.
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| 关 键 词： | 特征方程 根与系数关系 微分算子 积分形式特解 |
Integral Form of the Particular Solution for High Order Constant Coefficient LDE |
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| LIU Ling. Integral Form of the Particular Solution for High Order Constant Coefficient LDE[J]. Studies In College Mathematics, 2011, 14(1): 73-74 |
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| Authors: | LIU Ling |
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| Affiliation: | LIU Ling (School of Science, University of ShangHai for Science and Technology, Shanghai 200090,PRC) |
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| Abstract: | Abstract： By the relation of roots and coefficients for a characteristic equation, we provide an integral form of the particular solution for high order constant coefficient linear difference equation. In particular, a recurrent formula for the equation with the free term of the form f（x） = Pm（x）e^λx （where Pm（x） is a polynomial of degree m） is given. |
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| Keywords: | characteristic equation differential operator relation of roots and coefficients integral form of the particular solution |
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