\[ \left (x^2+1\right ) y''(x)+y'(x)^2+1=0 \] ✓ Mathematica : cpu = 0.153014 (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 = 0.33 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\frac {x}{{\it \_C1}}}+\ln \left ( {\it \_C1}\,x-1 \right ) +{\frac {\ln \left ( {\it \_C1}\,x-1 \right ) }{{{\it \_C1}}^{2}}}+{\it \_C2} \right \} \]