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Let \( y=y(x) \) be the solution of the differential equation,
P \( x \frac{d y}{d x}+y=x \log _{e} x,(x1) \).If \( 2 y(2)=\log _{e} 4-1 \), then \( y \)

W)
(e) is equal to :
[JEE Main - 2019 (January)]
(a) \( -\frac{\mathrm{e}}{2} \)
(b) \( -\frac{\mathrm{e}^{2}}{2} \)
(c) \( \frac{\mathrm{e}}{4} \)
(d) \( \frac{\mathrm{e}^{2}}{4} \)
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