\[ \left (y(x)^2+1\right ) y''(x)+(1-2 y(x)) y'(x)^2=0 \] ✓ Mathematica : cpu = 0.218294 (sec), leaf count = 46
\[\left \{\left \{y(x)\to \frac {i \left (1-c_1{}^{2 i} (x+c_2){}^{2 i}\right )}{1+c_1{}^{2 i} (x+c_2){}^{2 i}}\right \}\right \}\] ✓ Maple : cpu = 0.903 (sec), leaf count = 11
\[y \relax (x ) = \tan \left (\ln \left (c_{1} x +c_{2}\right )\right )\]