\[ \sqrt {a y''(x)^2+b y'(x)^2}+c y(x) y''(x)+d y'(x)^2=0 \] ✗ Mathematica : cpu = 9.49023 (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 = 1.715 (sec), leaf count = 116
\[ \left \{ y \left ( x \right ) =0,y \left ( x \right ) ={\it \_C1},y \left ( x \right ) ={\it \_C1}\,x+{\it \_C2},y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ {\frac {{\it \_b} \left ( {\it \_a} \right ) }{-{c}^{2}{{\it \_a}}^{2}+a} \left ( \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) \left ( -{c}^{2}{{\it \_a}}^{2}+a \right ) -cd{\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) +\sqrt { \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}a{d}^{2}-b \left ( -{c}^{2}{{\it \_a}}^{2}+a \right ) } \right ) }=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]