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Let y= y (x), x gt 1, be the solution of...

Let `y= y (x), x gt 1`, be the solution of the differential equation `(x- 1) (dy)/(dx) + 2xy = (1)/(x-1)`, with `y (2) = (1+ e^(4))/(2e^(4))`. If `y (3)= (e^(alpha) +1)/(beta e^(alpha))`, then the value of `alpha + beta` is equal to _____

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