\[ y''(x)-a \left (y'(x)^2+1\right )^{3/2}=0 \] ✓ Mathematica : cpu = 0.154454 (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 = 1.751 (sec), leaf count = 41
\[y \relax (x ) = \frac {\left (-1+\left (x +c_{1}\right )^{2} a^{2}\right ) \sqrt {-\frac {1}{-1+\left (x +c_{1}\right )^{2} a^{2}}}+c_{2} a}{a}\]