$${ x }^{ 2 } \displaystyle\frac{d}{d x } y = { x }^{ 2 } +xy- { y }^{ 2 }$$
$x=\frac{\left(-\sqrt{5}-1\right)y}{2}$
$x=\frac{\left(\sqrt{5}-1\right)y}{2}$
$y=\frac{\left(\sqrt{5}+1\right)x}{2}$
$y=\frac{\left(1-\sqrt{5}\right)x}{2}$
