JEE Main 2022 · 25 Jul · Shift 2, Mathematics question 25

Let $y=y(x)$ be the solution of the differential equation
$$\frac{dy}{dx}=\frac{4y^3+2yx^2}{3xy^2+x^3},\quad y(1)=1.$$
If for some $n\in\mathbb N$, $y(2)\in[n-1,n)$, then $n$ is equal to ______.