二阶常系数线性非齐次微分方程特解简易求法  

Simplification for Particular Solution of Second Order Linear Non-homogeneous Differential Equation with Constant Coefficients

作　　者：王海菊[1] 

机构地区：[1]北京联合大学基础部,北京100101

出　　处：《北京联合大学学报》2011年第2期73-75,共3页Journal of Beijing Union University

摘　　要：求二阶常系数线性非齐次微分方程特解通常是采用待定系数法,计算量很大。本文在不脱离教材特解的求法,利用推导特解过程中出现的重要式子Q″(x)+(2λ+p)Q'(x)+(λ2+pλ+q)Q(x)=Pm(x),简化待定系数法求特解的过程。对右端非齐次项eλx[Pl(x)cosωx+Pn(x)sinωx]是先设变换,化简右端非齐次项。The particular solution of second order linear non-homogeneous differential equation with constant coefficients is by means of undermined coefficients,which is relatively complex.Instead of using the method of particular solution in teaching materials,important formula in deducing particular solution is adopted.The solution of the problem can be simplified.

关 键 词：微分方程 特解 待定系数法 

分 类 号：O241.8[理学—计算数学]