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