Answer
$y=ce^{-x}-e^{-2x}$
Work Step by Step
We are given:
$y'+y=e^{-2x}$
The general solution of the equation can be given by:
$y=e^{-\int dx}(c+\int e^{\int dx}e^{-2x} dx)$
where $c$ is the constant of integration.
So:
$y=e^{-x}(c+\int e^{-x} dx)$
Simplify:
$y=ce^{-x}-e^{-2x}$
