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If the solution curve f(x,y)=0 of the di...

If the solution curve `f(x,y)=0` of the differential equation `(1+log_e x)(dx)/(dy)-xlog_e x=e^y , x gt 0` , passes through the points `(1,0)` and `(alpha,2)` then `(alpha)^(alpha)` is equal to

A

`e^(sqrt2 e^2)`

B

`e^(2 e^2)`

C

`e^(e^2)`

D

`e^(2 e^(sqrt2))`

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