Find the general solution to y′+2y=4e−2xy' + 2y = 4e^{-2x}y′+2y=4e−2x.
y=(4x+C)e−2xy = (4x + C)e^{-2x}y=(4x+C)e−2x
y=4x+Cy = 4x + Cy=4x+C
y=Ce−2x+4y = Ce^{-2x} + 4y=Ce−2x+4
y=Ce2x+4xy = Ce^{2x} + 4xy=Ce2x+4x