Answer
$$y = 2{e^{2x}} + C$$
Work Step by Step
$$\eqalign{
& \frac{{dy}}{{dx}} = 4{e^{2x}} \cr
& {\text{Separating variables leads to}} \cr
& dy = 4{e^{2x}}dx \cr
& {\text{To solve this equation}}{\text{, determine the antiderivative of each side}} \cr
& \int {dy} = \int {4{e^{2x}}dx} \cr
& {\text{rewrite the integral on the right side}} \cr
& \int {dy} = 2\int {{e^{2x}}\left( 2 \right)dx} \cr
& {\text{integrating by using }}\int {{e^u}du} = {e^u} + C{\text{ and the power rule }} \cr
& y = 2{e^{2x}} + C \cr} $$
