\[ \left (x^2+1\right ) y''(x)+y'(x)^2+1=0 \] ✓ Mathematica : cpu = 0.168383 (sec), leaf count = 33
\[\left \{\left \{y(x)\to -x \cot (c_1)+\csc ^2(c_1) \log (-x \sin (c_1)-\cos (c_1))+c_2\right \}\right \}\] ✓ Maple : cpu = 1.01 (sec), leaf count = 27
\[y \relax (x ) = \frac {x}{c_{1}}+\ln \left (c_{1} x -1\right )+\frac {\ln \left (c_{1} x -1\right )}{c_{1}^{2}}+c_{2}\]