\[ \left (x^2+1\right ) y''(x)+y'(x)^2+1=0 \] ✓ Mathematica : cpu = 0.101208 (sec), leaf count = 33
\[\left \{\left \{y(x)\to -x \cot \left (c_1\right )+\csc ^2\left (c_1\right ) \log \left (-x \sin \left (c_1\right )-\cos \left (c_1\right )\right )+c_2\right \}\right \}\] ✓ Maple : cpu = 0.204 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\frac {x}{{\it \_C1}}}+\ln \left ( {\it \_C1}\,x-1 \right ) +{\frac {\ln \left ( {\it \_C1}\,x-1 \right ) }{{{\it \_C1}}^{2}}}+{\it \_C2} \right \} \]