常系数非齐次线性微分方程的特解探究

Special solution of nonhomogeneous linear differential equations with constant coefficients

本文针对求常系数非齐次线性微分方程的特解进行了探究,根据右端函数f(x)的三种不同的pm(x),e^λxpm(x),e^αx[pm1(x)cosβx+pm2(x)]类型,给出其伴随方程概念,都统一到第一种类型pm(x)上来,两种通过对m+1元线性方程组的求解,得到常系数非齐次线性微分方程的特解,关键思路是求伴随方程的解。还可以用来求某些不定积分,简化积分计算过程。

In this paper,the special solution of the non-homogeneous linear differential equation of constant coefficient is explored.According to the three different types of right-end functions,the concept of the accompanying equation is given,and all of them are unified to the first type.Two special solutions to non-homogeneous linear differential equations with constant coefficients are obtained by solving m+1 linear equations.The key idea is to find the solution of the accompanying equation.It can also be used to find some indefinite integrals and simplify the integral calculation process.