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