Let y=y(x), x>1, be the solution of the differential equation (x-1) (d y)/(d x)+2 x y=1/(x-1), with y(2)=(1+e^4)/(2 e^4). If y(3)=(e^α+1)/(β e^α),…

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