Find the general solution to y′=ex−y+e−yy' = e^{x-y} + e^{-y}y′=ex−y+e−y given y(0)=0y(0) = 0y(0)=0.
ey=ex+Ce^y = e^x + Cey=ex+C
ey=ex+1e^y = e^x + 1ey=ex+1
e−y=ex+Ce^{-y} = e^x + Ce−y=ex+C
ey=x+Ce^y = x + Cey=x+C