利用线性变换求线性常系数非齐次微分方程的特解  

Solving Particular Solutions of Constant Coefficient Non-Homogeneous Nth Order Linear Differential Equations by Linear Transformations

作　　者：滕延燕[1] 吉喆[2] 

机构地区：[1]青岛理工大学理学院,青岛266033 [2]青岛理工大学土木工程学院,青岛266033

出　　处：《青岛理工大学学报》2010年第4期104-106,共3页Journal of Qingdao University of Technology

摘　　要：线性常系数非齐次微分方程y（n）＋a1y（n-1）＋…＋any=eλx[Pl（x）cosωx＋Pn（x）sinωx]的特解y＊一般采用待定系数法求解,但待定系数求解需要计算y＊的1至n阶导数,这相当麻烦.笔者引入一个线性变换,把y＊的1至n阶导数表示成向量的内积,而不必计算出这些导数,从而较大的减少了计算量,最后给出了一个详细的应用实例.An undetermined coefficient is a general method of solving the particular solution y＊ of a non-homogeneous nth order linear differential equation y（n）＋a1y（n-1）＋…＋any=eλx[Pl（x）cosωx＋Pn（x）sinωx].This method needs to compute the 1st to nth order derivatives,which is very complex.In the paper these derivatives are expressed by a linear transform into dot products of vectors without being computed any more,which fairly reduces the complexity of calculation.In conclusion,an exemplary application of this method is given.

关 键 词：微分方程 线性变换 特解 

分 类 号：O175.1[理学—数学]