\[ \sqrt {a y''(x)^2+b y'(x)^2}+c y(x) y''(x)+d y'(x)^2=0 \] ✗ Mathematica : cpu = 10.3769 (sec), leaf count = 0 , could not solve
DSolve[d*Derivative[1][y][x]^2 + c*y[x]*Derivative[2][y][x] + Sqrt[b*Derivative[1][y][x]^2 + a*Derivative[2][y][x]^2] == 0, y[x], x]
✓ Maple : cpu = 1.172 (sec), leaf count = 116
\[\left \{y \left (x \right ) = 0, y \left (x \right ) = c_{1}, y \left (x \right ) = c_{1} x +c_{2}, y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} , \left [\left \{\frac {\left (-\textit {\_a} c d \textit {\_}b\left (\textit {\_a} \right )+\left (-c^{2} \textit {\_a}^{2}+a \right ) \left (\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right )+\sqrt {a \,d^{2} \textit {\_}b\left (\textit {\_a} \right )^{2}-\left (-c^{2} \textit {\_a}^{2}+a \right ) b}\right ) \textit {\_}b\left (\textit {\_a} \right )}{-c^{2} \textit {\_a}^{2}+a}=0\right \}, \left \{\textit {\_a} =y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {d}{d x}y \left (x \right )\right \}, \left \{x =c_{1}+\int \frac {1}{\textit {\_}b\left (\textit {\_a} \right )}d \textit {\_a} , y \left (x \right )=\textit {\_a} \right \}\right ]\right )\right \}\]