\[ x \left (\sqrt {x y(x)}-1\right ) y'(x)-y(x) \left (\sqrt {x y(x)}+1\right )=0 \] ✓ Mathematica : cpu = 0.199599 (sec), leaf count = 23
\[\text {Solve}\left [c_1+\log (x)=\frac {2}{\sqrt {x y(x)}}+\log (y(x)),y(x)\right ]\]
✓ Maple : cpu = 0.014 (sec), leaf count = 33
\[ \left \{ -{1 \left ( 1+ \left ( {\it \_C1}-\ln \left ( x \right ) +{\frac {\ln \left ( xy \left ( x \right ) \right ) }{2}} \right ) \sqrt {xy \left ( x \right ) } \right ) {\frac {1}{\sqrt {xy \left ( x \right ) }}}}=0 \right \} \]