\[ \boxed { x \left ( y \left ( x \right ) \ln \left ( xy \left ( x \right ) \right ) +y \left ( x \right ) -ax \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \left ( ax\ln \left ( xy \left ( x \right ) \right ) -y \left ( x \right ) +ax \right ) =0} \]
Mathematica: cpu = 0.054007 (sec), leaf count = 24 \[ \text {Solve}\left [a x \log (x y(x))-y(x) \log (x y(x))=c_1,y(x)\right ] \]
Maple: cpu = 0.202 (sec), leaf count = 19 \[ \left \{ \left ( xy \left ( x \right ) \right ) ^{-ax+y \left ( x \right ) }-{\it \_C1}=0 \right \} \]