\[ x y'(x) \left (2 x^2 y(x) \log (y(x))+1\right )-2 y(x)=0 \] ✓ Mathematica : cpu = 0.230414 (sec), leaf count = 35
\[\text {Solve}\left [\frac {y(x)}{x^2}+2 \left (\frac {1}{2} y(x)^2 \log (y(x))-\frac {y(x)^2}{4}\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.097 (sec), leaf count = 36
\[\{y \left (x \right ) = {\mathrm e}^{\RootOf \left (2 \textit {\_Z} \,x^{2} {\mathrm e}^{2 \textit {\_Z}}+2 c_{1} x^{2}-x^{2} {\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}}\right )}\}\]