What is the general solution for the linear first-order equation y′+y=e−xy' + y = e^{-x}y′+y=e−x?
y=(x+C)exy = (x+C)e^xy=(x+C)ex
y=(x+C)e−xy = (x+C)e^{-x}y=(x+C)e−x
y=xe−x+Cy = x e^{-x} + Cy=xe−x+C
y=e−x+Cexy = e^{-x} + C e^xy=e−x+Cex