xdy/dx-y=x²+y²
两边除以x^2得
(xy'-y)/x^2=(x²+y²)/x^2=1+(y/x)^2
(y/x)'=1+(y/x)^2
令y/x=t,则t'=1+t^2
dt/(1+t^2)=dx
两边积分得
arctant=x+C
即arctan(y/x)=x+C