For $ x \; \epsilon \;R, x ≠ 0,$ if $y(x)$ is a differentiable function such that $\begin{align*} x \int_1^x y\; (t) \;dt = (x+1) \int_1^x t\; y \;(t)\; dt, \end{align*}$ then $y(x) $ equals : (where C is a constant.)

Question

$\begin{array}{1 1} (1)\; \frac{C}{x} e^{-\frac{1}{x}} \\ (2)\; \frac{C}{x^2} e^{-\frac{1}{x}} \\ (3)\; \frac{C}{x^3} e^{-\frac{1}{x}} \\ (4)\; Cx^3 e^{\frac{1}{x}} \end{array} $