\[ \sqrt {a y''(x)^2+b y'(x)^2}+c y(x) y''(x)+d y'(x)^2=0 \] ✗ Mathematica : cpu = 14.6301 (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 = 0.441 (sec), leaf count = 94
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) +{\frac {{\it \_b} \left ( {\it \_a} \right ) }{{c}^{2}{{\it \_a}}^{2}-a} \left ( {\it \_a}\,cd{\it \_b} \left ( {\it \_a} \right ) -\sqrt {{{\it \_a}}^{2}b{c}^{2}+ \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}a{d}^{2}-ab} \right ) }=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]