Solve y′′−4y′+4y=0y'' - 4y' + 4y = 0y′′−4y′+4y=0.
y=(C1+C2x)e2xy = (C_1 + C_2 x) e^{2x}y=(C1+C2x)e2x
y=C1e2x+C2e−2xy = C_1 e^{2x} + C_2 e^{-2x}y=C1e2x+C2e−2x
y=C1cos2x+C2sin2xy = C_1 \cos 2x + C_2 \sin 2xy=C1cos2x+C2sin2x
y=e2xy = e^{2x}y=e2x