\[ y''(x)-a \left (y'(x)^2+1\right )^{3/2}=0 \] ✓ Mathematica : cpu = 0.173018 (sec), leaf count = 75
\[\left \{\left \{y(x)\to c_2-\frac {i \sqrt {a^2 x^2+2 a c_1 x-1+c_1{}^2}}{a}\right \},\left \{y(x)\to \frac {i \sqrt {a^2 x^2+2 a c_1 x-1+c_1{}^2}}{a}+c_2\right \}\right \}\] ✓ Maple : cpu = 2.365 (sec), leaf count = 41
\[\left \{y \left (x \right ) = \frac {c_{2} a +\left (\left (c_{1}+x \right )^{2} a^{2}-1\right ) \sqrt {-\frac {1}{\left (c_{1}+x \right )^{2} a^{2}-1}}}{a}\right \}\]