一类二阶常系数非齐次线性微分方程特解的求解研究

对于二阶常系数非齐次线性微分方程 y″ +py′ + qy =f(x) ,当 f(x) =Pn(x)eαx或 f(x) =eλxPn(x)cosωx+euxsinβx时 ,本文给出了求特解的简易方法 ,并且这种方法易于在计算机上进行编程计算。因此 ,利用这种方法可以圆满地解决此类微分方程求特解的实际计算上的问题

On finding a special solution of a kind of second-order constant coefficients non-homogeneous linear differential equation

This paper is devoted to provide a formule of finding a special solution of differential equation\{ y″+py′+qy\}=f(x) with f(x) taking the following forms f(x)=P n(x)e\+ αx or f(x)=e λx P n(x) cos wx+\{e ux P m(x) sin βx\}. This method is easy to calculate with computer.