| 一类变系数高阶线性齐次微分方程解的探求(英文) |
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| 摘 要： | 本文对系数全为多项式和广义多项式的n阶线性齐次微分方程引入特征方程的概念。给出了具有指数型解的充要条件，推广了经典的常系数线性方程和著名的Euler方程的的解法，为求解变系数线性微分方程提供了有效的方法。
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| 关 键 词： | 系数全为多项式的线性齐次微分方程 特征方程 特征根 求解 |
The Search for a Class of High Order Variable Coefficient Linear Homogeneous Differential Equation solution |
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| Authors: | Zhang Xueyuan |
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| Institution: | Hunan Textile College |
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| Abstract: | In this paper,the concept of characteristic equation is leaded into n-order linear homogereous differential equation which coefficients are all multino-mial (or extendecd multinomial)and a necessary and sufficient condition for indexspecial solution is given. This extend the solutions of clossical constant coefficientlinear equation and the famous Euler equation and provide a effective method forsolving variable coefficient linear differential equation. |
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| Keywords: | Linear homogeneous differential equation which coefficients are all multinomial Characteristic equation characteristic root solution |
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