\[ \left (y(x)^2+1\right ) y''(x)+(1-2 y(x)) y'(x)^2=0 \] ✓ Mathematica : cpu = 0.0825091 (sec), leaf count = 14
\[\left \{\left \{y(x)\to \tan \left (\log \left (c_1 \left (c_2+x\right )\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.053 (sec), leaf count = 11
\[ \left \{ y \left ( x \right ) =\tan \left ( \ln \left ( {\it \_C1}\,x+{\it \_C2} \right ) \right ) \right \} \]