\[ y''(x)-a \sqrt {y'(x)^2+1}=0 \] ✓ Mathematica : cpu = 0.0968086 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {\cosh (c_1) \cosh (a x)}{a}+\frac {\sinh (c_1) \sinh (a x)}{a}+c_2\right \}\right \}\] ✓ Maple : cpu = 0.913 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={\frac {\cosh \left ( a \left ( x+{\it \_C1} \right ) \right ) }{a}}+{\it \_C2} \right \} \]