Answer
$y=2x+e^{-x}-1$
Work Step by Step
We are given that $\dfrac{dy}{dx}=2-e^{-x}$
We will separate the variables to obtain:
$ \ dy=(2-e^{-x}) \ dx$
Integrate to obtain:
$\int \ dy=\int (2-e^{-x}) \ dx$
This implies that $y=2x+e^{-x}+C$
After applying the initial conditions, $y=0$ when $x=0$, we get $C=-1$
Therefore, we have: $y=2x+e^{-x}-1$
