Find the general solution to y′+y=xe−xy' + y = x e^{-x}y′+y=xe−x.
y=(x22+C)e−xy = (\frac{x^2}{2} + C)e^{-x}y=(2x2+C)e−x
y=(x2+C)exy = (x^2 + C)e^xy=(x2+C)ex
y=x22e−x+Cy = \frac{x^2}{2} e^{-x} + Cy=2x2e−x+C
y=(x+C)e−xy = (x+C)e^{-x}y=(x+C)e−x