The coupled system in two variables $x(t)$ and $y(t)$
$$\frac{dx}{dt}=-xy,\ \ \ \frac{dy}{dt}=-y+x^2-2y^2$$
has the exact slow manifold $y=x^2$ on which the evolution is $$\frac{dx}{dt}=-x^3.$$
Could you please anyone explain to me how we got this result?