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 _____________.

Question

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 _____________.

Correct Answer

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