Let \( y = y(x),\; x>1 \), be the solution of the differential equation \( (x-1)\frac{dy}{dx} + 2xy = \frac{1}{x-1} \) with \( y(2) = \frac{1+e^{4}}{2e^{4}} \). If \( y(3) = \frac{e^{\alpha}+1}{\beta e^{\alpha}} \), then the value of \( \alpha + \beta \) is equal to ______.
