\[ y''(x)-a \left (y'(x)^2+1\right )^{3/2}=0 \] ✓ Mathematica : cpu = 0.0639292 (sec), leaf count = 75
\[\left \{\left \{y(x)\to c_2-\frac {i \sqrt {a^2 x^2+2 a c_1 x+c_1^2-1}}{a}\right \},\left \{y(x)\to c_2+\frac {i \sqrt {a^2 x^2+2 a c_1 x+c_1^2-1}}{a}\right \}\right \}\]
✓ Maple : cpu = 0.129 (sec), leaf count = 55
\[ \left \{ y \left ( x \right ) ={\frac { \left ( a{\it \_C1}+ax+1 \right ) \left ( a{\it \_C1}+ax-1 \right ) }{a}\sqrt {- \left ( {{\it \_C1}}^{2}{a}^{2}+2\,{\it \_C1}\,{a}^{2}x+{a}^{2}{x}^{2}-1 \right ) ^{-1}}}+{\it \_C2} \right \} \]