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Differential Equations question

2022 · 28 Jun · Shift 2 · Q31

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JEE Main
Mathematics
Differential Equations
2022 · 28 Jun · Shift 2 · Q31

Differential Equations question

2022 · 28 Jun · Shift 2 · Q31

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

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 :

A
$e{\log _e}(2)$
B
$- e{\log _e}(2)$
C
${e^2}{\log _e}(2)$
D
$- {e^2}{\log _e}(2)$

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