Solution
= Solution
For the specified <polynomial>,
$$
F_y=2(y-x^2),\qquad F_x=-4x(y-x^2)-5x^4.
$$
The first equation $F_y=0$ forces $y=x^2$; substitution into $F_x=0$ then gives $x=0$, and hence $y=0$. It also satisfies the curve equation. Therefore the unique <singular point> is
$$
\boxed{(x,y)=(0,0)}.
$$