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Differential Equations question

2021 · 18 Mar · Shift 2 · Q23

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JEE Main
Mathematics
Differential Equations
2021 · 18 Mar · Shift 2 · Q23

Differential Equations question

2021 · 18 Mar · Shift 2 · Q23

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

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

{{dy} \over {dx}} = (y + 1)\left( {(y + 1){e^{{x^2}/2}} - x} \right)

, 0 < x < 2.1, with y(2) = 0. Then the value of

{{dy} \over {dx}}

at x = 1 is equal to :

A
${{{e^{5/2}}} \over {{{(1 + {e^2})}^2}}}$
B
${{5{e^{1/2}}} \over {{{({e^2} + 1)}^2}}}$
C
$- {{2{e^2}} \over {{{(1 + {e^2})}^2}}}$
D
${{ - {e^{3/2}}} \over {{{({e^2} + 1)}^2}}}$

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