方程两边分别取对数,化为
1/2 ln(x^2+y^2)=arctan(y/x)
两边对x求导,(1/2)(2x+2yy')/(x^2+y^2)=(xy'-y)/x^2/(1+y^2/x^2)
整理得y'=(x+y)/(x-y)
故dy=(x+y)/(x-y)dx
方程两边分别取对数,化为
1/2 ln(x^2+y^2)=arctan(y/x)
两边对x求导,(1/2)(2x+2yy')/(x^2+y^2)=(xy'-y)/x^2/(1+y^2/x^2)
整理得y'=(x+y)/(x-y)
故dy=(x+y)/(x-y)dx