\[ y''(x)-a \sqrt {y'(x)^2+1}=0 \] ✓ Mathematica : cpu = 0.10916 (sec), leaf count = 30
DSolve[-(a*Sqrt[1 + Derivative[1][y][x]^2]) + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {\cosh (c_1) \cosh (a x)}{a}+\frac {\sinh (c_1) \sinh (a x)}{a}+c_2\right \}\right \}\] ✓ Maple : cpu = 2.038 (sec), leaf count = 16
dsolve(diff(diff(y(x),x),x)-a*(diff(y(x),x)^2+1)^(1/2)=0,y(x))
\[y \left (x \right ) = \frac {\cosh \left (a \left (x +c_{1}\right )\right )}{a}+c_{2}\]