ODE No. 1679

\[ \left (x^2+1\right ) y''(x)+y'(x)^2+1=0 \]

✓ Mathematica : cpu = 0.178772 (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 = 0.125 (sec), leaf count = 26

dsolve((x^2+1)*diff(diff(y(x),x),x)+diff(y(x),x)^2+1=0,y(x))

\[y \left (x \right ) = \frac {x}{c_{1}}+\frac {\left (c_{1}^{2}+1\right ) \ln \left (x c_{1} -1\right )}{c_{1}^{2}}+c_{2}\]