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If \(\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{{2}^{\mathrm{x}+\mathrm{y}}-{2}^{\mathrm{x}}}{{2}^{\mathrm{y}}},\mathrm{y}\le…

Q1

If \(\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{{2}^{\mathrm{x}+\mathrm{y}}-{2}^{\mathrm{x}}}{{2}^{\mathrm{y}}},\mathrm{y}\left(0\right)=1\), then \(y(1)\) is equal to:

[JEE Main 2021, 31 Aug (Shift 1)]

a

\({\log }_{2}(1+\mathrm{e})\)

b

\({\log }_{2}(2+\mathrm{e})\)

c

\({\log }_{2}\left(1+{\mathrm{e}}^{2}\right)\)

d

\({\log }_{2}(2\mathrm{e})\)

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