\[ x y(x) y''(x)-2 x y'(x)^2+(y(x)+1) y'(x)=0 \] ✓ Mathematica : cpu = 0.0635551 (sec), leaf count = 37
\[\left \{\left \{y(x)\to \frac {\tan \left (\frac {\sqrt {c_1} \left (\log (x)-c_2\right )}{\sqrt {2}}\right )}{\sqrt {2} \sqrt {c_1}}\right \}\right \}\]
✓ Maple : cpu = 0.195 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\tanh \left ( {\frac {\ln \left ( x \right ) -{\it \_C2}}{2\,{\it \_C1}}} \right ) \right \} \]