Differential Equations

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 \(n \in \mathbb{N}, y(2) \in[n-1, n)\), then \(n\) is equal to _____________.