\[ x y(x) y''(x)-2 x y'(x)^2+(y(x)+1) y'(x)=0 \] ✓ Mathematica : cpu = 0.0707471 (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 = 1.406 (sec), leaf count = 18
\[\left \{y \left (x \right ) = c_{1} \tanh \left (\frac {-c_{2}+\ln \left (x \right )}{2 c_{1}}\right )\right \}\]