Find the general solution to the differential equation y′+y=e−xy' + y = e^{-x}y′+y=e−x.
y(x)=(x+C)e−xy(x) = (x + C)e^{-x}y(x)=(x+C)e−x
y(x)=xe−x+Cy(x) = xe^{-x} + Cy(x)=xe−x+C
y(x)=e−x+Cexy(x) = e^{-x} + Ce^xy(x)=e−x+Cex
y(x)=(x+C)exy(x) = (x + C)e^xy(x)=(x+C)ex