Chapter 7: Transcendental Functions - Section 7.4 - Exponential Change and Separable Differential Equations - Exercises 7.4 - Page 400: 9

$\dfrac{2}{3}y^{\frac{3}{2}}-\sqrt x=C$

As we are given that $2 \sqrt{xy} \dfrac{dy}{dx}=1$ Thus, $\sqrt y dy=\dfrac{dx}{(2 \sqrt x)}$ Need to integrate the above expression, that is, $\sqrt y dy=\dfrac{dx}{(2 \sqrt x)}$. Thus, $\int \sqrt y dy= \int \dfrac{dx}{2 \sqrt x}$ or, $\dfrac{2}{3}y^{\frac{3}{2}}=\sqrt x +C$ Hence, $\dfrac{2}{3}y^{\frac{3}{2}}-\sqrt x=C$