JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 22

Let $y=y(x)$, $x>1$, be the solution of the differential equation $(x-1)\dfrac{dy}{dx}+2xy=\dfrac1{x-1}$, with $y(2)=\dfrac{1+e^4}{2e^4}$. If $y(3)=\dfrac{e^\alpha+1}{\beta e^\alpha}$, then the value of $\alpha+\beta$ is equal to ______.