\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -a\sqrt { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1}=0} \]
Mathematica: cpu = 0.023503 (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 = 0.125 (sec), leaf count = 18 \[ \left \{ y \left ( x \right ) ={\frac {\cosh \left ( {\it \_C1}\,a+ax \right ) }{a}}+{\it \_C2} \right \} \]