# Question #3d111

Feb 5, 2017

$y \left(x\right) = \sqrt[3]{\frac{3 {x}^{4}}{2} + C}$

#### Explanation:

This is a separable differential equation, so we can solve it by separating the variables on the two sides and then integrating:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2 {x}^{3}}{y} ^ 2$

${y}^{2} \mathrm{dy} = 2 {x}^{3} \mathrm{dx}$

$\int {y}^{2} \mathrm{dy} = 2 \int {x}^{3} \mathrm{dx}$

These are standard integrals we can solve using the power rule:

${y}^{3} / 3 = 2 {x}^{4} / 4 + C$

${y}^{3} = \frac{3 {x}^{4}}{2} + C$

and finally:

$y = \sqrt[3]{\frac{3 {x}^{4}}{2} + C}$