Differential Equations: JEE Main 2026 Mathematics question

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