\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( y \left ( x \right ) -a\ln \left ( y \left ( x \right ) \right ) x+{x}^{2} \right ) y \left ( x \right ) }{ \left ( -y \left ( x \right ) \ln \left ( y \left ( x \right ) \right ) -y \left ( x \right ) \ln \left ( x \right ) -y \left ( x \right ) +ax \right ) x}}=0} \]
Mathematica: cpu = 0.089511 (sec), leaf count = 33 \[ \text {Solve}\left [a x \log (y(x))-\frac {x^2}{2}-y(x) \log (x)-y(x) \log (y(x))=c_1,y(x)\right ] \]
Maple: cpu = 0.343 (sec), leaf count = 30 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( -2\,{\it \_Z}\,ax+2\,\ln \left ( x \right ) {{\rm e}^{{\it \_Z}}}+2\,{\it \_Z}\, {{\rm e}^{{\it \_Z}}}+2\,{\it \_C1}\,a+{x}^{2} \right ) }} \right \} \]