Lagrange插值法在一类非齐线性常微分方程中的应用

Application of Lagrange Interpolation to a Class of the Nonhomogeneous Linear Differential Equations with Constant Coefficints

利用等价方程组,Lagrange插值多项式与常数变易公式,研究了一类n阶常系数非齐线性常微分方程P(D)y=a(x)cos eλχ+b(x)sin eμχ,得到了这种方程的一种新的求解方法,并给出了一个详细的实例.

The nth order nonhomogeneous linear differential equation with constant coeffients P（D）y=a（x） cos e^λx＋b（x） sin e^μλ , Where P （D）=D^n＋a1D^n-1＋... ＋ an-1D＋a, is differential polynomial operator, a2 , a2,..., an.λ and μ are arbitrary constants, a（x） and b（x） are continuous functions, is investigated by using equivalent system, Lagrange interpolation polynomial and variation of constants formula, A new method for solving this equation is obtained. Finally, an illustrative example is presented in detail.