\[ y(x) \left (x^2 y(x)^2+1\right )+x (x y(x)-1)^2 y'(x)=0 \] ✓ Mathematica : cpu = 0.0706054 (sec), leaf count = 24
\[\text {Solve}\left [c_1+\frac {1}{x y(x)}+2 \log (y(x))=x y(x),y(x)\right ]\]
✓ Maple : cpu = 0.208 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{{\it RootOf} \left ( -2\,{{\rm e}^{{\it \_Z}}}\ln \left ( x \right ) -{{\rm e}^{2\,{\it \_Z}}}+2\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+2\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+1 \right ) }}}{x}} \right \} \]