\[ y(x) \left (x^2 y(x)^2+1\right )+x (x y(x)-1)^2 y'(x)=0 \] ✓ Mathematica : cpu = 0.147247 (sec), leaf count = 25
\[\text {Solve}\left [x y(x)-\frac {1}{x y(x)}-2 \log (y(x))=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.235 (sec), leaf count = 34
\[y \relax (x ) = \frac {{\mathrm e}^{\RootOf \left (-{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} \ln \relax (x )+2 \,{\mathrm e}^{\textit {\_Z}} c_{1}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )}}{x}\]