Answer
$$y = {x^3} + 3{x^2} + C$$
Work Step by Step
$$\eqalign{
& \frac{{dy}}{{dx}} = 3{x^2} + 6x \cr
& {\text{Separating variables leads to}} \cr
& dy = \left( {3{x^2} + 6x} \right)dx \cr
& {\text{To solve this equation}}{\text{, determine the antiderivative of each side}} \cr
& \int {dy} = \int {\left( {3{x^2} + 6x} \right)dx} \cr
& {\text{integrating by using the power rule we obtain}} \cr
& y = 3\left( {\frac{{{x^3}}}{3}} \right) + 6\left( {\frac{{{x^2}}}{2}} \right) + C \cr
& {\text{simplifying}} \cr
& y = {x^3} + 3{x^2} + C \cr} $$
