用待定系数法求非齐次欧拉方程的特解

Finding out Special Solutions for Inhomogeneous Euler Equations by Using of Indeterminate Coefficients

直接用待定系数法详细地讨论了两类常见的二阶非齐次欧拉方程x2y″+axy′+by=xαPm(lnx),x2y″+axy′+by=xα[Ps(lnx)cos(βlnx)+Pn(lnx)sin(βlnx)],特解的求法,并对求n阶非齐次欧拉方程的特解作了必要的说明.

In this paper, by using of indeterminate coefficients, we discuss in detail how to find out the special sc＇utions for the following two classes of inhomogeneous Euler equations of order 2 x2y＇＇＋axy＇＋by=xαPm（lnx）,x2y＇＇＋axy＇＋by=xα[Px（lnx）cos（βlnx）＋Pn（lnx）sin（βlnx）], Moreover, we give also some necessary illustrations of special solution for inhomogeneous Euler equations of order n.