Differential Equations

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