\[ y''(x)-a \sqrt {y'(x)^2+1}=0 \] ✓ Mathematica : cpu = 0.0213716 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {\sinh \left (c_1\right ) \sinh (a x)}{a}+\frac {\cosh \left (c_1\right ) \cosh (a x)}{a}+c_2\right \}\right \}\]
✓ Maple : cpu = 0.249 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={\frac {\cosh \left ( a{\it \_C1}+ax \right ) }{a}}+{\it \_C2} \right \} \]