Let y=y(x) be a differentiable function in the interval (0, ∞) such that y(1)=2, and lim_t → x((t^2 y(x)-x^2 y(t))/(x-t))=3 for each x>0. Then 2 y(2)…

Let $\displaystyle y=y(x)$ be a differentiable function in the interval $\displaystyle (0, \infty)$ such that $\displaystyle y(1)=2$, and $\displaystyle \lim _{t \rightarrow x}\left(\frac{t^2 y(x)-x^2 y(t)}{x-t}\right)=3$ for each $\displaystyle x>0$. Then $\displaystyle 2 y(2)$ is equal to