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If `y =y(x)` is the solution of the differential equation `(dy)/(dx)+(4x)/(x^2-1)y =(x+2)/((x^2-1)^(5/2)),x gt 1` such that `f(2) + 2/9log _e (2+sqrt3)` and `y(sqrt2) = alpha log_e (sqrt (alpha) + beta)+beta -sqrt gamma,alpha gamma in NN` , then `alpha beta gamma ` is equal to__.

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