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