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The solution curve of the differential equation,
\( \mathrm{P} \)
\( \left(1+e^{-x}\right)\left(1+y^{2}\right) \frac{d y}{d x}=y^{2} \), which passes through the point
W
\( (0,1) \), is
[JEE Main-2020 (September)]
(a) \( \mathrm{y}^{2}+1=\mathrm{y}\left(\log _{\mathrm{e}}\left(\frac{1+\mathrm{e}^{-\mathrm{x}}}{2}\right)+2\right) \)
(b) \( \mathrm{y}^{2}+1=\mathrm{y}\left(\log _{\mathrm{e}}\left(\frac{1+\mathrm{e}^{\mathrm{x}}}{2}\right)+2\right) \)
(c) \( \mathrm{y}^{2}=1+\mathrm{y} \log _{\mathrm{e}}\left(\frac{1+\mathrm{e}^{-\mathrm{x}}}{2}\right) \)
(d) \( \mathrm{y}^{2}=1+\mathrm{y} \log _{\mathrm{e}}\left(\frac{1+\mathrm{e}^{\mathrm{x}}}{2}\right) \)
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