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Differential Equations question

2019 · 11 Jan · Shift 1 · Q24

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JEE Main
Mathematics
Differential Equations
2019 · 11 Jan · Shift 1 · Q24

Differential Equations question

2019 · 11 Jan · Shift 1 · Q24

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

If y(x) is the solution of the differential equation

{{dy} \over {dx}} + \left( {{{2x + 1} \over x}} \right)y = {e^{ - 2x}},\,\,x \gt 0,\,

where

y\left( 1 \right) = {1 \over 2}{e^{ - 2}},

then

A
y(loge2) = loge4
B
y(x) is decreasing in (0, 1)
C
y(loge2) = ${{{{\log }_e}2} \over 4}$
D
y(x) is decreasing in $\left( {{1 \over 2},1} \right)$

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