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Let the solution curve y= y(x) of the di...

Let the solution curve y= y(x) of the differential equation
`[x/(sqrt(x^2-y^2))+e^(y/x)]x(dy)/(dx)=x+[x/(sqrt(x^2-y^2))+e^(y/x)]y`
pass through the points (1,0) and `(2alpha, alpha) alpha > 0`. Then a is equal to

A

`1/2exp(pi/6+sqrte-1)`

B

`1/2exp(pi/3+e-1)`

C

`exp(pi/6+sqrte+1)`

D

`2exp(pi/3+sqrte-1)`

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