\[ \boxed { \left ( \sqrt {xy \left ( x \right ) }-1 \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( \sqrt {xy \left ( x \right ) }+1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.080510 (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 = 0.015 (sec), leaf count = 31 \[ \left \{ \ln \left ( x \right ) -{\it \_C1}-{\frac {1}{2} \left ( \ln \left ( xy \left ( x \right ) \right ) \sqrt {xy \left ( x \right ) }+2 \right ) {\frac {1}{\sqrt {xy \left ( x \right ) }}}}=0 \right \} \]