Solve and get solutions : $\bigg( x +y \large\frac{dy}{dx}\bigg)=\bigg( y -x \large\frac{dy}{dx}\bigg) \bigg(x^4+\large\frac{y^6}{x^2}$$+3 (x^2y^2+y^4)\bigg)$

Question

$(a)\;\frac{y}{x} -\frac{2}{(x^2+y^2)^2}=c' \\ (b)\;\frac{4y}{x} -\frac{1}{(x^2+y^2)^2}=c' \\ (c)\;2y -\frac{1}{(x^2+y^2)^2}=c' \\ (d)\;2yx -\frac{1}{(x^2+y^2)^2}=c'$