Let \( \mathrm{y}=\mathrm{f}(\mathrm{x}) \) is the solution of the ...

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Let \( \mathrm{y}=\mathrm{f}(\mathrm{x}) \) is the solution of the differential equation \( e^{\mathrm{y}} \)
\( P \) \( \left(\frac{d y}{d x}-1\right)=e^{x} \) such that \( y(0)=0 \), then \( y(1) \) is equal to

W)
(a) \( 2 \mathrm{e} \)
[JEE Main-2020 (January)]
(c) \( \log _{e} 2 \)
(b) \( 1+\log _{e} 2 \)
(d) \( 2+\log _{e} 2 \)
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