用常数变易法接微分方程

Question

如题所述

Answer 1

(1)
dy/dx = y+sinx
y' -y = sinx
let
yg= Ce^x
yp= Asinx+Bcosx
yp' = Acosx -Bsinx
yp'-yp = sinx
(-A-B)sinx +(A-B)cosx = sinx
-A-B=1 (1)
A-B=0 (2)
(1)+(2)
B= -1/2
(2)-(1)
A =-1/2
ie
y = yg+yp
=Ce^x - (1/2)sinx -(1/2)cosx