返回上页 下页下页方程 ypyqy?e?x[Pl (x)cos?x?Pn(x)sin?x]的特解形式?
应用欧拉公式可得
e?x[Pl(x)cos?x?Pn(x)sin?x]
]2)(2)([ ieexPeexPe xixinxixilx
xinlxinl exiPxPexiPxP )()( )]()([21)]()([21
xixi exPexP )()( )()(
其中 )(21)( iPPxP nl )(21)( iPPxP nl 而 m? m a x { l? n }?
返回上页 下页返回方程 ypyqy?e?x[Pl (x)cos?x?Pn(x)sin?x]的特解形式?
应用欧拉公式可得
e?x[Pl(x)cos?x?Pn(x)sin?x]
设方程 ypyqy?P(x)e(i?)x的特解为 y1*?xkQm(x)e(i?)x?
P(x)e(i?)x +?P(x)e(i?)x?
则?P(x)e(i?)x的特解Qm(x)e(i?)x必是方程 ypyqyy1*?xk
其中当i?不是特征方程的根时 k取 0?否则取 1?
因此方程 ypyqy?e?x[Pl(x)cos?x?Pn(x)sin?x]的特解为
y1*?xkQm(x)e(i?)x?xk?Qm(x)e(i?)x
xke?x[Qm(x)(cos?x?i sin?x)Qm(x)(cos?x?i sin?x)]
xk e?x[R(1)m(x)cos?x?R(2)m(x)sin?x]?