#### Answer

$$y = {x^4} + {x^6} + C$$

#### Work Step by Step

$$\eqalign{
& \frac{{dy}}{{dx}} = 4{x^3} + 6{x^5} \cr
& {\text{Separating variables leads to}} \cr
& dy = \left( {4{x^3} + 6{x^5}} \right)dx \cr
& {\text{To solve this equation}}{\text{, determine the antiderivative of each side}} \cr
& \int {dy} = \int {\left( {4{x^3} + 6{x^5}} \right)dx} \cr
& {\text{integrating by using the power rule we obtain}} \cr
& y = 4\left( {\frac{{{x^4}}}{4}} \right) + 6\left( {\frac{{{x^6}}}{6}} \right) + C \cr
& {\text{simplifying}} \cr
& y = {x^4} + {x^6} + C \cr} $$