方程y"+py+q=e[P(x) COSO+Pn(x) )sina]的特解形式: 应用欧拉公式可得 eAx[P(x)coax+P()sinop(x)e tio)x+ p()e(-iojx 设方程y"+py+q=P(x)eo的特解为y1*=xQn(x)l(+o), 则y1*=xQn(x)(1)必是方程y+py+q=P(x)e(k-o的特解, 其中当io不是特征方程的根时k取0,否则取1 因此方程y"+py+y=eAPx) COAx+Pn(x)inox的特解为 I*=xem()e(tio)x+x2m(x)e-i@)xr =xkeAr[om(x(cos sinox)+o(x)(cos @x-isinox) -xke[Rom(x)coax+R2m(x)sinox 上页 下页上页 返回 下页 方程y+py+qy=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y+py+qy=P(x)e (+i)x的特解为y1 *=x kQm (x)e (+i)x  =P(x)e (+i)x +P(x)e (−i)x  则 P(x)e Q (−i)x的特解 m (x)e y1 *=x (−i)x必是方程y+py+qy= k 其中当i不是特征方程的根时k取0否则取1 因此方程y+py+qy=e x [Pl (x)cosx+Pn (x)sinx]的特解为 y1 *=x kQm (x)e (+i)x+x k Qm (x)e (−i)x =x ke x [Qm (x)(cosx+isinx)+Qm (x)(cosx−isinx)] =x k e x [R(1) m (x)cosx+R(2) m (x)sinx]