Answer
$${\text{The answer is option }}\left( {\bf{d}} \right)$$
Work Step by Step
$$\eqalign{
& y' - 2y = 0 \cr
& {\text{Write }}y'{\text{ as }}\frac{{dy}}{{dx}} \cr
& \frac{{dy}}{{dx}} - 2y = 0 \cr
& {\text{Separate the variables}} \cr
& \frac{{dy}}{{dx}} = 2y \cr
& \frac{{dy}}{y} = 2dx \cr
& {\text{Integrate both sides}} \cr
& \int {\frac{{dy}}{y}} = \int 2 dx \cr
& \ln \left| y \right| = 2x + {C_1} \cr
& {e^{\ln \left| y \right|}} = {e^{2x}}{e^{{C_1}}} \cr
& y = C{e^{2x}} \cr
& {\text{The answer is option }}\left( {\bf{d}} \right) \cr} $$
