\[ y(x) \left (x^2 y(x)^2+1\right )+x (x y(x)-1)^2 y'(x)=0 \] ✓ Mathematica : cpu = 0.0667557 (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 = 0.241 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{{\it RootOf} \left ( -{{\rm e}^{2\,{\it \_Z}}}-2\,\ln \left ( x \right ) {{\rm e}^{{\it \_Z}}}+2\,{\it \_C1}\,{{\rm e}^{{\it \_Z}}}+2\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+1 \right ) }}}{x}} \right \} \]