\[ y''(x)-a \left (y'(x)^2+1\right )^{3/2}=0 \] ✓ Mathematica : cpu = 0.139914 (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 = 0.507 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={\frac {1}{a} \left ( \left ( -1+ \left ( x+{\it \_C1} \right ) ^{2}{a}^{2} \right ) \sqrt {- \left ( -1+ \left ( x+{\it \_C1} \right ) ^{2}{a}^{2} \right ) ^{-1}}+a{\it \_C2} \right ) } \right \} \]