Existence, Uniqueness & Bifurcations · Superchallenge problem

Let $f(y) = y^2\sin\dfrac1y$ for $y \ne 0$ and $f(0) = 0$. Let $y(t)$ solve $y' = f(y)$ with $y(0) = \dfrac15$. Find $\displaystyle\lim_{t\to\infty}y(t)$.