方程y″+py′+qy=e^(λx)[P_l(x)shωx+Q_n(x)chωx]解法探析  

Exploration and Analysis on Solution of Equation y″+py′+qy=e^(λx)[P_l(x)shωx+Q_n(x)chωx]

作　　者：王有文 WANG You-wen(Department of Fundamental Courses,Shanxi Institute of Technology,Yangquan 045000,Shanxi,China)

机构地区：[1]山西工程技术学院基础部,山西阳泉045000

出　　处：《兰州文理学院学报（自然科学版）》2018年第2期41-44,共4页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：对方程y″+py′+qy=e^(λx)[P_l(x)shωx+Q_n(x)chωx]的求解方法进行了探析.首先推导出了方程特解的多项式满足的两个方程与一个相关特征方程,其次根据l、n的大小关系、λ与特征根的关系分类确定了多项式的次数,再次结合三个例题具体说明了如何求特解,最后得出了结论.Solution of equation y″+py′+qy=eλx[P l(x)shωx+Q n(x)chωx]is explored and analyzed in this paper.Firstly,polynomials which are included in particular solution of nonhomogeneous equation should meet two equations,so these equations and a related characteristic equation are deduced;secondly,degrees of polynomials are ascertained in accordance with relation between l、n,λand characteristic roots;thirdly,three examples and their solving process are given to show specific process of finding particular solutions.

关 键 词：非齐次方程 特解 特征方程 多项式次数 双曲函数 

分 类 号：O151.21[理学—数学]