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Differential Equations question

2021 · 25 Jul · Shift 1 · Q30

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JEE Main
Mathematics
Differential Equations
2021 · 25 Jul · Shift 1 · Q30

Differential Equations question

2021 · 25 Jul · Shift 1 · Q30

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

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

{{dy} \over {dx}} = 1 + x{e^{y - x}}, - \sqrt 2 \lt x \lt \sqrt 2 ,y(0) = 0

then, the minimum value of

y(x),x \in \left( { - \sqrt 2 ,\sqrt 2 } \right)

is equal to :

A
$\left( {2 - \sqrt 3 } \right) - {\log _e}2$
B
$\left( {2 + \sqrt 3 } \right) + {\log _e}2$
C
$\left( {1 + \sqrt 3 } \right) - {\log _e}\left( {\sqrt 3 - 1} \right)$
D
$\left( {1 - \sqrt 3 } \right) - {\log _e}\left( {\sqrt 3 - 1} \right)$

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