常系数非齐次线性微分方程组的初等解法

Elementary Solution to Systems of Inhomogeneous LDE with Constant Coefficients

利用初等变换将常系数非齐次线性微分方程组化为由若干个相互独立的高阶常系数非齐次线性微分方程组成的方程组,再利用高阶常系数齐次线性微分方程的特征根法和非齐次方程的待定系数法求该方程组的基本解组及特解,最后通过初等变换求原方程组的基本解组及特解,从而可求出其通解.

By elementary transformation, the systems ＇of inhomogeneous linear differential equations with constant coefficients can be changed into some independent systems of higher order inhomogeneous linear differential equations with constant coefficients. Then, By the method of characteristic root of higher order homogeneous linear differential equation with constant coefficient and the method of undetermined coefficient of higher order inhomogeneous linear differential equation with constant coefficient, the fundamental set of solutions and the special solution of this system can be obtained. Finally, by the elementary transformation, the fundamental set of solutions and the special solution and then general solution of the primal systems can be obtained.