常系数非齐次线性微分方程
一、f ( x ) e Pm ( x )型其中Pm ( x ) a0 x m a1 x m 1 am 1 x am考虑 y* Q( x )e , Q( x )是某个待定多项式, 则( y*) Q ( x )e x Q( x ) e x e x [ Q( x ) Q ( x )]( y*) e x [ 2 Q( x ) 2 Q ( x ) Q ( x )] x
x
代入(1), 得e x [ 2 Q( x ) 2 Q ( x ) Q ( x )] x x pe [ Q( x ) Q ( x )] qQ( x )e e Pm ( x ) x3