Determine the integrating factor μ(x)\mu(x)μ(x) for y′+y=xy' + y = xy′+y=x and the resulting solution.
μ=ex\mu = e^xμ=ex, y=x−1+Ce−xy = x - 1 + Ce^{-x}y=x−1+Ce−x
μ=e−x\mu = e^{-x}μ=e−x, y=x+1+Ce−xy = x + 1 + Ce^{-x}y=x+1+Ce−x
μ=x\mu = xμ=x, y=12x+C/xy = \frac{1}{2}x + C/xy=21x+C/x
μ=ex\mu = e^xμ=ex, y=x+1+Ce−xy = x + 1 + Ce^{-x}y=x+1+Ce−x