find the implicit solution of $$\frac{2xy}{(x^2+y^2)^2}dx+(1+\frac{y^2-x^2}{(x^2+y^2)^2})dy=0$$, with equation $$x^2+y^2=1$$
substitute the equation and rearrange: $$2xdx=-(\frac{1+y^2-x^2}{y})dy$$, I sub the equation of $$x^2=1-y^2$$, I have $$2xdx=-2ydy$$ the implicit solution is $$\sqrt{-x^2-c}=y$$
Am I right?