第四题怎么解，微分方程

(4)
y'''+py''+qy'+ry =0
y=2e^(-x) +e^x.sinx
y'=-2e^(-x) +(sinx+cosx)e^x
y''=2e^(-x) +(sinx+cosx + cosx- sinx)e^x = 2e^(-x) +2cosx.e^x
y'''=-2e^(-x) +2(cosx-sinx).e^x
y'''+py''+qy'+ry =0
-2e^(-x) +2(cosx-sinx).e^x +2pe^(-x) +2pcosx.e^x -2qe^(-x) +q(sinx+cosx)e^x
+2re^(-x) +re^x.sinx =0
(-2+2p-2q+2r).e^(-x) + [ (2+2p+q)cosx +(-2+q+r)sinx]e^x =0
-2+2p-2q+2r=0 (1)
2+2p+q=0 (2)
-2+q+r=0 (3)
(2)-(1)

4+3q-2r=0 (4)
2(3)+(4)
q=0
from (3)
-2+q+r=0
r=2
from (2)
2+2p+q=0
2+2p=0
p=-1
(p,q,r)=(-1,0, 2)