Existence, Uniqueness & Bifurcations · Superchallenge problem

Let $y(t)$ solve $y' = -y^3 + y^5$ with $y(0) = \dfrac12$. The solution tends to the equilibrium $0$, but since $f'(0) = 0$ the approach is not exponential. Find $\displaystyle\lim_{t\to\infty} t\,y(t)^2$.