Solution to the differential equation \( \frac{dy}{dx} + 2y = e^{-x} \), \( y(0) = 1 \)
This is a first-order linear non-homogeneous differential equation. The general form is:
\[ \frac{dy}{dx} + P(x)y = Q(x) \]
Here, \( P(x) = 2 \) and \( Q(x) = e^{-x} \).
