\[ y''(x)-a \sqrt {y'(x)^2+1}=0 \] ✓ Mathematica : cpu = 0.118697 (sec), leaf count = 36
DSolve[-(a*Sqrt[1 + Derivative[1][y][x]^2]) + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {e^{a x+c_1} \left (1+e^{-2 a x-2 c_1}\right )}{2 a}+c_2\right \}\right \}\] ✓ Maple : cpu = 0.758 (sec), leaf count = 16
dsolve(diff(diff(y(x),x),x)-a*(diff(y(x),x)^2+1)^(1/2)=0,y(x))
\[y \left (x \right ) = c_{2}+\frac {\cosh \left (a \left (x +c_{1}\right )\right )}{a}\]