# Chapter 10 - Differential Equations - Chapter Review - Review Exercises - Page 561: 26

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

#### 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}

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