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If \( y(x) \) is the solution of the differential equation
\( P \) \( \frac{d y}{d x}+\left(\frac{2 x+1}{x}\right) y=e^{-2 x}, x0 \) where \( y(1)=\frac{1}{2} e^{-2} \), then

W)
[JEEMain - 2019 (January)]
(a) \( y\left(\log _{\mathrm{e}} 2\right)=\log _{\mathrm{e}} 4 \)
(b) \( y\left(\log _{\mathrm{e}} 2\right)=\frac{\log _{\mathrm{e}} 2}{4} \)
(c) \( y(x) \) is decreasing in \( \left(\frac{1}{2}, 1\right) \)
(d) \( \mathrm{y}(\mathrm{x}) \) is decreasing in \( (0,1) \)
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