\[ y''(x)-a \left (y'(x)^2+1\right )^{3/2}=0 \] ✓ Mathematica : cpu = 0.0685451 (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 = 0.143 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={\frac {1}{a} \left ( \left ( -1+ \left ( x+{\it \_C1} \right ) ^{2}{a}^{2} \right ) \sqrt {- \left ( -1+ \left ( x+{\it \_C1} \right ) ^{2}{a}^{2} \right ) ^{-1}}+{\it \_C2}\,a \right ) } \right \} \]