\[ \boxed { \sqrt {a \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) ^{2}+b \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}}+cy \left ( x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +d \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 14.719369 (sec), leaf count = 44 \[ \text {DSolve}\left [\sqrt {a y''(x)^2+b y'(x)^2}+c y(x) y''(x)+d y'(x)^2=0,y(x),x\right ] \]
Maple: cpu = 0.297 (sec), leaf count = 94 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( { \it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) +{\frac { {\it \_b} \left ( {\it \_a} \right ) }{{c}^{2}{{\it \_a}}^{2}-a} \left ( {\it \_a}\,cd{\it \_b} \left ( {\it \_a} \right ) -\sqrt {{{\it \_a}}^{2 }b{c}^{2}+ \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}a{d} ^{2}-ab} \right ) }=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) , {\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]