\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) + \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1=0} \]
Mathematica: cpu = 0.032504 (sec), leaf count = 27 \[ \text {DSolve}\left [y^{(3)}(x)+y(x) y''(x)-y'(x)^2+1=0,y(x),x\right ] \]
Maple: cpu = 0.453 (sec), leaf count = 73 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {{\rm d}^{2}}{{\rm d}{{\it \_a}}^{2}}}{\it \_b } \left ( {\it \_a} \right ) \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}{\it \_b} \left ( {\it \_a} \right ) + \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( { \it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) {\it \_a} - \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+1=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( { \it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]