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

Sep 4, 2016

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

#### Explanation:

This is separable

$y ' = \frac{x + \sin x}{3 {y}^{2}}$

$3 {y}^{2} \setminus y ' = x + \sin x$

$\int 3 {y}^{2} \setminus y ' \setminus \mathrm{dx} = \int x + \sin x \setminus \mathrm{dx}$

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

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

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