摘要
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.
出处
《湖南城市学院学报(自然科学版)》
CAS
2005年第4期34-36,共3页
Journal of Hunan City University:Natural Science
关键词
非齐线性常微分方程
等价方程组
基解矩阵
LAGRANGE插值多项式
常数变易公式
Nonhomogeneous linear ordinary differential equation
equivalent system
fundamental solution matrix
lagrange interpolation polynomial
variation of constants formula