Let x = x(y) be the solution of the differential equation $2y\,{e^{x/{y^2}}}dx + \left( {{y^2} - 4x{e^{x/{y^2}}}} \right)dy = 0$ such that x(1) = 0. Then, x(e) is equal to :

Question

Let x = x(y) be the solution of the differential equation

$2y\,{e^{x/{y^2}}}dx + \left( {{y^2} - 4x{e^{x/{y^2}}}} \right)dy = 0$ such that x(1) = 0. Then, x(e) is equal to :

$e{\log _e}(2)$

$ - e{\log _e}(2)$

${e^2}{\log _e}(2)$

$ - {e^2}{\log _e}(2)$

Solution

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