Solve y′′−y=0y'' - y = 0y′′−y=0.
y=C1ex+C2e−xy = C_1 e^x + C_2 e^{-x}y=C1ex+C2e−x
y=C1cosx+C2sinxy = C_1 \cos x + C_2 \sin xy=C1cosx+C2sinx
y=(C1+C2x)exy = (C_1 + C_2 x) e^xy=(C1+C2x)ex
y=Cexy = C e^xy=Cex