\[ \left (x^2+y(x)^2\right ) y''(x)+\left (y(x)-x y'(x)\right ) \left (y'(x)^2+1\right )=0 \] ✓ Mathematica : cpu = 0.325658 (sec), leaf count = 74
\[\text {Solve}\left [\frac {1}{2} \left (\log \left (1-\frac {i y(x)}{x}\right )+\log \left (1+\frac {i y(x)}{x}\right )+i \cot (c_1) \left (\log \left (1-\frac {i y(x)}{x}\right )-\log \left (1+\frac {i y(x)}{x}\right )\right )\right )=-\log (x)+c_2,y(x)\right ]\] ✓ Maple : cpu = 1.961 (sec), leaf count = 82
\[\left \{y \left (x \right ) = x \tan \left (\RootOf \left (x^{\frac {2}{c_{1}-1}} \left (\cos ^{2}\left (\textit {\_Z} \right )\right ) {\mathrm e}^{\frac {2 c_{2}}{c_{1}-1}}-x^{\frac {2 c_{1}}{c_{1}-1}} {\mathrm e}^{\frac {2 i \textit {\_Z}}{c_{1}-1}} {\mathrm e}^{\frac {2 i c_{1} \textit {\_Z}}{c_{1}-1}} {\mathrm e}^{\frac {2 c_{1} c_{2}}{c_{1}-1}}\right )\right )\right \}\]