\[ y'(x)=\frac {y(x) \left (-a x \log (y(x))+x^2+y(x)\right )}{x (a x-y(x)-y(x) \log (x)-y(x) \log (y(x)))} \] ✓ Mathematica : cpu = 0.519897 (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 = 1.353 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( -2\,ax{\it \_Z}+2\,{{\rm e}^{{\it \_Z}}}\ln \left ( x \right ) +2\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+2\,{\it \_C1}\,a+{x}^{2} \right ) }} \right \} \]