解微分方程(x-y+1)dy⼀dx=1?

2025-06-22 07:30:05
推荐回答(2个)
回答1:

(x-y+1)dy/dx=1
dx/dy = x-y +1
dx/dy -x = -y+1
let
xg= Ae^y
xp= By +C
xp' =B
xp' -xp = -y+1
B-(By +C) = -y +1
-By +(B-C) = -y +1
B=1 and B-C=1
B=1 and C=0
xg=y
通解
x= xg+xp =Ae^y +y

回答2: