The solution to the differential equation \( y\left(n y+x y^{\prime...

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The solution to the differential equation \( y\left(n y+x y^{\prime}=0\right. \), where \( \mathrm{y}(1)=\mathrm{e} \), is
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(a) \( x(\ln y)=1 \)
(b) \( x y(\ln y)=1 \)
(c) \( (\ln y)^{2}=2 \)
(d) \( \ln \mathrm{y}+\left(\frac{\mathrm{x}^{2}}{2}\right) \mathrm{y}=1 \)
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