一类高阶常微分方程的特解公式

Special Solution Formula for a Class of Higher Order Ordinary Differential Equation

对高阶方程d^nx/dt^n+a_1d^(n-1)x/dt^(n-1)+…+a_(n-1)dx/dt+a_nx=e^(λt)(Acosωt+Bsinωt),利用待定系数法和复数法得到了当λ+iω不是特征根时特解的一般公式,并给出了详细推导过程和若干具体算例。

Based on the undetermined coefficient a nd complex number methods, this paper obtains he general formula of the special solution for the higher order ordinary differential equationd^nx/dt^n＋a d^n-1x/dt^n-1＋…＋an.dx/dt＋anx=c^n（Acoswt＋Bsinwt） when the eigenvalue. The proofsdtn dtn dtnd practical examples are also given in detail.