# How to you find the general solution of dy/dx=(x^2+2)/(3y^2)?

Jan 12, 2017

y(x) = root(3)(x^3/3+2x+C

#### Explanation:

This is a separable differential equation, so we can proceed by separating the variables and integrating:

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

$3 {y}^{2} \mathrm{dy} = \left({x}^{2} + 2\right) \mathrm{dx}$

$\int 3 {y}^{2} \mathrm{dy} = \int \left({x}^{2} + 2\right) \mathrm{dx}$

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

y(x) = root(3)(x^3/3+2x+C