#### Answer

$y=e^{-x}(\sin x-\cos x)+ce^{-2x}$

#### Work Step by Step

Here, we have $y'+2y=2e^{-x} \sin x$
The integrating factor is: $I=e^{\int 2 dx}=e^{2x}$
Now, $e^{2x}[y'+2y]=2 (e^{2x}) (e^{-x}) (\sin x)$
This implies that
$\int [e^{2x}y]' =\int 2e^{x}\sin x dx$
Hence, $y=e^{-x}(\sin x-\cos x)+ce^{-2x}$