Answer
$\dfrac{2}{3}y^{\frac{3}{2}}-\sqrt x=C$
Work Step by Step
We have: $2 \sqrt{xy} \dfrac{dy}{dx}=1$
or, $\sqrt y dy=\dfrac{dx}{2 \sqrt x}$
We have to integrate the above expression:
$\int \sqrt y dy= \int \dfrac{dx}{2 \sqrt x}$
or, $\dfrac{2}{3}y^{\frac{3}{2}}=\sqrt x +C$
This implies:
$\dfrac{2}{3}y^{\frac{3}{2}}-\sqrt x=C$
