摘要
设方程y″+py′+qy=e^(λx )P_(m)(x)有特解y*=R(x)eλx,P_(m)(x)为m次多项式.当λ是特征方程单根时,R′(x)是m次多项式,R(x)是m+1次多项式.对比R(x)=(ax+b)R_(m)(x)和R(x)=xR_(m)(x)两种假设(R_(m)(x)为m次多项式),对后者的合理性进行分析,并证明按后者所得特解是唯一存在的.
Let y*=R(x)e^(λx )be the special solution of y″+py′+qy=e^(λx )P_(m)(x),P_(m)(x)is an m-degree polynomial.Ifλis the single root of characteristic equation,then R′(x)is an m-degree polynomial and R(x)is an m+1-degree polynomial.The two hypotheses R(x)=(ax+b)R_(m)(x)and R(x)=xR_(m)(x)are compared(R_(m)(x)is an m-degree polynomial),rationality of the latter is analyzed,and the special solution corresponds to the latter is proved to be unique.
作者
鲁琦
LU Qi(School of Science and Physics,Bengbu University,Bengbu Anhui 233030,China)
出处
《兰州工业学院学报》
2021年第6期82-84,共3页
Journal of Lanzhou Institute of Technology
基金
安徽省高校自然科学研究重点项目(KJ2017A569)。
关键词
微分方程
特解
特征方程
differential equation
special solution
characteristic equation