Solve y′=e−x−yy' = e^{-x} - yy′=e−x−y with y(0)=0y(0) = 0y(0)=0.
y=xe−xy = xe^{-x}y=xe−x
y=e−xy = e^{-x}y=e−x
y=x+e−xy = x+e^{-x}y=x+e−x
y=1−e−xy = 1-e^{-x}y=1−e−x