\[ x y'(x) (-a x+y(x)+y(x) \log (x y(x)))-y(x) (a x \log (x y(x))+a x-y(x))=0 \] ✓ Mathematica : cpu = 0.0828397 (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 = 9.489 (sec), leaf count = 19
\[ \left \{ \left ( xy \left ( x \right ) \right ) ^{-ax+y \left ( x \right ) }-{\it \_C1}=0 \right \} \]