Putzer方法在一类n阶常系数非齐线性常微分方程P(D)x=acose^(λt)+bsine^(μt)中的应用

Applications of Putzer Method to a Kind of Nonhomogeneous nth Order Linear Ordinary Differential Equations P(D)x=acose^(λt)+bsine^(μt) with Constant Coefficients

利用等价方程组和Putzer方法,研究了n阶常系数非齐线性常微分方程P(D)x=acoseλt+bsineμt,得到了这种方程的一种新的求解方法,最后给出了一个详细的实例.

In this paper, using equivalent system and Putzer method, we study a nonhomogeneous nth order linear ordinary differential equations P(D)x=acos eλt+bsin eμt with constant coefficients where P(D)=Dn+a1Dn-1+…+an-1D+an, D=tdd, a1, …an, a, b, λ, μ are arbitrary real constants. We obtain a new method of finding solution of initial value problem to the above equation and present an illustrative example at the end of this paper.