Explanation

(c)
Given, $\frac{dy}{dx} = \left( \frac{y}{x}\ \right)^{1/3}$
$\Rightarrow \ \frac{dy}{dx} = \frac{y^{1/3}}{x^{1/3}}\ \Rightarrow \frac{dy}{y^{1/3}} = \frac{dx}{x^{1/3}}$
On integrating both sides, we get
$\int_{}^{}{\frac{dy}{y^{1/3}} =}\int_{}^{}\frac{dy}{x^{1/3}}$
$\Rightarrow \ \frac{y^{2/3}}{\frac{2}{3}} = \frac{x^{2/3}}{\frac{2}{3}} + c_{1}$
$\Rightarrow \frac{3}{2}y^{2/3} = \frac{3}{2}x^{2/3} + c_{1}$
$\Rightarrow \ y^{2/3} - x^{2/3} = c$ $(where\ c = \frac{2}{3}c_{1})$