Jordan标准型在非齐线性常微分方程中的应用

Application of Jordan Canonical Form to Nonhomogeneous Linear Ordinary Differential Equations

利用等价方程组,Jordan标准型与常数变易公式,研究了一类n阶常系数非齐线性常微分方程P(D)y=a(x)coseλx+b(x)sineμx,得到了它的一种新的求解方法.最后给出了一个详细的实例.

In this paper, the nth order nonhomogeneous linear ordinary differential equations with constant coefficints P（D）y=a（x）cose^λx＋b（x）sine^μx , Where P（D） = D^n ＋a1D^n-1 ＋...＋an-1D＋an is differential polynomial operator, a1, a2,..., an, A and μ are arbitrary constants, a（x） and b（x） are continuous functions and it is investigated by using equivalent system, Jordan canonical form and variation of constants formula. A new method of finding its solution is obtained. Finally, an illustrative example is presented in detail.