解:
dx/dt = x+ sint
dx/dt - x = sint
let
xp = Asint +Bcost
xp'= Acost -Bsint
xp' - xp= sint
(A-B)sint +(A+B)cost =sint
A-B =1 (1)
A+B=0 (2)
(2)-(1)
B = -1/2
(1)+(2)
A= 1/2
ie
x = Ce^(t) + (1/2)sint -(1/2)cost
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