Solve dydx=ex−y+e−y\frac{dy}{dx} = e^{x-y} + e^{-y}dxdy=ex−y+e−y for y(0)=0y(0)=0y(0)=0.
ey=ex+Ce^y = e^x + Cey=ex+C
ey=exe^y = e^xey=ex
ey=ex+0e^y = e^x + 0ey=ex+0
ey=ex+1e^y = e^x + 1ey=ex+1