令x+y=u,y=u-x,y'=u'-1方程可化为u'-1=1/uu'=(u+1)/uudu/(u+1)=dx[1- 1/(u+1)]du=dxu-ln|u+1|=x+Cx+y-ln|x+y+1|=x+Cy-ln|x+y+1|=C
如图