\[ y'(x)=\frac {y(x) \left (-a x \log (y(x))+x^2+y(x)\right )}{x (a x-y(x)-y(x) \log (x)-y(x) \log (y(x)))} \] ✓ Mathematica : cpu = 0.575128 (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 = 0.584 (sec), leaf count = 30
\[y \relax (x ) = {\mathrm e}^{\RootOf \left (-2 \textit {\_Z} a x +2 \ln \relax (x ) {\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} a +x^{2}\right )}\]