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The solution of the differential equation
[JEE Main-2020 (September)]
P \( \frac{d y}{d x}-\frac{y+3 x}{\log _{e}(y+3 x)}+3=0 \) is :
(where \( \mathrm{C} \) is a constant of integration.)
(a) \( \mathrm{x}-\frac{1}{2}\left(\log _{e}(\mathrm{y}+3 \mathrm{x})\right)^{2}=\mathrm{C} \)
(b) \( \mathrm{y}+3 \mathrm{x}-\frac{1}{2}\left(\log _{\mathrm{e}} \mathrm{x}\right)^{2}=\mathrm{C} \)
(c) \( \mathrm{x}-2 \log _{e}(\mathrm{y}+3 \mathrm{x})=\mathrm{C} \)
(d) \( \mathrm{x}-\log _{\mathrm{e}}(\mathrm{y}+3 \mathrm{x})=\mathrm{c} \)
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