Let y = y(x) be the solution of the differential equation \(\frac{\mathrm{dy}}{\mathrm{dx}}=1+{\mathrm{xe}}^{\mathrm{y}-…

Let y = y(x) be the solution of the differential equation \(\frac{\mathrm{dy}}{\mathrm{dx}}=1+{\mathrm{xe}}^{\mathrm{y}-\mathrm{x}},-\sqrt{2}<\mathrm{x}<\sqrt{2},\mathrm{y}(0)=0\) then, the minimum value of \(\mathrm{y}(\mathrm{x}),\mathrm{x}\in (-\sqrt{2},\sqrt{2})\) is equal to:

[JEE Main 2021, 25 Jul (Shift 1)]