\[ x \left (\sqrt {x y(x)}-1\right ) y'(x)-y(x) \left (\sqrt {x y(x)}+1\right )=0 \] ✓ Mathematica : cpu = 0.0817774 (sec), leaf count = 24
\[\text {Solve}\left [\frac {2}{\sqrt {x y(x)}}+\log (y(x))-\log (x)=c_1,y(x)\right ]\]
✓ Maple : cpu = 0.016 (sec), leaf count = 31
\[ \left \{ \ln \left ( x \right ) -{\it \_C1}-{\frac {1}{2} \left ( \ln \left ( xy \left ( x \right ) \right ) \sqrt {xy \left ( x \right ) }+2 \right ) {\frac {1}{\sqrt {xy \left ( x \right ) }}}}=0 \right \} \]