\[ x y(x) y''(x)-2 x y'(x)^2+(y(x)+1) y'(x)=0 \] ✓ Mathematica : cpu = 0.0639699 (sec), leaf count = 52
\[\left \{\left \{y(x)\to \frac {\tan \left (\frac {1}{2} \left (\sqrt {2} \sqrt {c_1} \log (x)-\sqrt {2} \sqrt {c_1} c_2\right )\right )}{\sqrt {2} \sqrt {c_1}}\right \}\right \}\] ✓ Maple : cpu = 0.213 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\tanh \left ( {\frac {\ln \left ( x \right ) -{\it \_C2}}{2\,{\it \_C1}}} \right ) \right \} \]