If \(\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{{2}^{\mathrm{x}}\mathrm{y}+{2}^{\mathrm{y}}\cdot {2}^{\mathrm{x}}}{{2}^{\math…

If \(\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{{2}^{\mathrm{x}}\mathrm{y}+{2}^{\mathrm{y}}\cdot {2}^{\mathrm{x}}}{{2}^{\mathrm{x}}+{2}^{\mathrm{x}+\mathrm{y}}{\log }_{\mathrm{e}}2},\mathrm{y}\left(0\right)=0\), then for \(y = 1\), the value of \(x\) lies in the interval:

[JEE Main 2021, 31 Aug (Shift 2)]