# What is a solution to the differential equation dy/dx=(x^2+2)/(4y^3)?

##### 1 Answer
Jul 18, 2016

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

#### Explanation:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{{x}^{2} + 2}{4 {y}^{3}}$

this is separable

$4 {y}^{3} \frac{\mathrm{dy}}{\mathrm{dx}} = {x}^{2} + 2$

$\int \setminus 4 {y}^{3} \frac{\mathrm{dy}}{\mathrm{dx}} \setminus \mathrm{dx} = \int \setminus {x}^{2} + 2 \setminus \mathrm{dx}$

$\int \setminus 4 {y}^{3} \setminus \mathrm{dy} = \int \setminus {x}^{2} + 2 \setminus \mathrm{dx}$

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

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