JEE Main 2022 · 26 Jul · Shift 2, Mathematics question 28

Suppose $y=y(x)$ be the solution curve to the differential equation $\dfrac{dy}{dx}-y=2-e^{-x}$ such that $\displaystyle\lim_{x\to\infty}y(x)$ is finite. If $a$ and $b$ are respectively the $x$- and $y$-intercepts of the tangent to the curve at $x=0$, then the value of $a-4b$ is equal to ______.