常系数非齐次线性微分方程的特解探究

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英文篇名：Special solution of nonhomogeneous linear differential equations with constant coefficients 作者：吴亚敏 英文作者：WU Ya-min;College of Mathematics and Statistics,Huanggang Normal University; 关键词：微分方程 ; 特征方程 ; 伴随方程 ; 线性方程组 英文关键词：differential equation;;characteristic equation;;accompanying equation;;linear equations 中文刊名：HGXB 英文刊名：Journal of Huanggang Normal University 机构：黄冈师范学院数学与统计学院; 出版日期：2019-06-10 出版单位：黄冈师范学院学报 年：2019 期：v.39;No.185 语种：中文; 页：HGXB201903007 页数：7 CN：03 ISSN：42-1275/G4 分类号：31-37

摘要

本文针对求常系数非齐次线性微分方程的特解进行了探究,根据右端函数f(x)的三种不同的p_m(x),e~(λx)p_m(x),e~(αx)[p_(m_1)(x)cosβx+p_(m_2)(x)]类型,给出其伴随方程概念,都统一到第一种类型p_m(x)上来,两种通过对m+1元线性方程组的求解,得到常系数非齐次线性微分方程的特解,关键思路是求伴随方程的解。还可以用来求某些不定积分,简化积分计算过程。
        In this paper, the special solution of the non-homogeneous linear differential equation of constant coefficient is explored. According to the three different types of right-end functions, the concept of the accompanying equation is given, and all of them are unified to the first type. Two special solutions to non-homogeneous linear differential equations with constant coefficients are obtained by solving m+1 linear equations. The key idea is to find the solution of the accompanying equation. It can also be used to find some indefinite integrals and simplify the integral calculation process.

引文

[1] 同济大学数学系.高等数学第七版上册[M].北京 :高等教育出版社,2014:338-359.
    [2] 黄立宏.高等数学(上)[M].北京:北京大学出版社,2018:237-248.
    [3] 杨继明,候雪炯.一类常系数非齐次线性微分方程的特解公式[J].大学数学,2008,24(6):184-186.
    [4] 余智君.二阶常系数非齐次线性微分方程通解的简易求法[J].重庆工学院学报,2008(8):85-86.
    [5] 彭艳芳.关于函数一致连续性的教学探究[J].黄冈师范学院学报,2017,37(6):65-67.
    [6] 金维栋.关于凸函数的等价命题[J].黄冈师范学院学报,1990,10(3):36-38.
    [7] 陈文略.一般奇异函数及其构造形式[J].黄冈师范学院学报,2016,36(6):16-18.