\[ \left (x^2+y(x)^2\right ) y''(x)-\left (x y'(x)-y(x)\right ) \left (y'(x)^2+1\right )=0 \] ✓ Mathematica : cpu = 0.257552 (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 = 2.132 (sec), leaf count = 82
\[ \left \{ y \left ( x \right ) =\tan \left ( {\it RootOf} \left ( - \left ( {{\rm e}^{{\frac {i{\it \_C1}\,{\it \_Z}}{-1+{\it \_C1}}}}} \right ) ^{2} \left ( {x}^{{\frac {{\it \_C1}}{-1+{\it \_C1}}}} \right ) ^{2} \left ( {{\rm e}^{{\frac {{\it \_C2}\,{\it \_C1}}{-1+{\it \_C1}}}}} \right ) ^{2} \left ( {{\rm e}^{{\frac {i{\it \_Z}}{-1+{\it \_C1}}}}} \right ) ^{2}+ \left ( \cos \left ( {\it \_Z} \right ) \right ) ^{2} \left ( {x}^{ \left ( -1+{\it \_C1} \right ) ^{-1}} \right ) ^{2} \left ( {{\rm e}^{{\frac {{\it \_C2}}{-1+{\it \_C1}}}}} \right ) ^{2} \right ) \right ) x \right \} \]