Let the solution curve $y = y(x)$ of the differential equation $\left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]x{{dy} \over {dx}} = x + \left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]y$ pass through the points (1, 0) and (2$\alpha$, $\alpha$), $\alpha$ > 0. Then $\alpha$ is equal to

Question

Let the solution curve $y = y(x)$ of the differential equation

$\left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]x{{dy} \over {dx}} = x + \left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]y$

pass through the points (1, 0) and (2$\alpha$, $\alpha$), $\alpha$ > 0. Then $\alpha$ is equal to

${1 \over 2}\exp \left( {{\pi \over 6} + \sqrt e - 1} \right)$

${1 \over 2}\exp \left( {{\pi \over 6} + e - 1} \right)$

$\exp \left( {{\pi \over 6} + \sqrt e + 1} \right)$

$2\exp \left( {{\pi \over 3} + \sqrt e - 1} \right)$

Solution

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