\[ x y'(x) (-a x+y(x)+y(x) \log (x y(x)))-y(x) (a x \log (x y(x))+a x-y(x))=0 \] ✓ Mathematica : cpu = 0.395319 (sec), leaf count = 24
\[\text {Solve}[a x \log (x y(x))-y(x) \log (x y(x))=c_1,y(x)]\] ✓ Maple : cpu = 0.312 (sec), leaf count = 19
\[\left (x y \relax (x )\right )^{-a x +y \relax (x )}-c_{1} = 0\]