令 x+y=u, y=u-x, y'=u'-1代入方程得
u'-1=u^2
du /(u^2+1) =dx
变量可分离,两边积分得通解 arctanu =x+C, u=tan(x+C),将 u=x+y 代入即可,y=tan(x+C)-x
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