\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) - \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) + \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.030004 (sec), leaf count = 25 \[ \text {DSolve}\left [y^{(3)}(x)-y(x) y''(x)+y'(x)^2=0,y(x),x\right ] \]
Maple: cpu = 0.655 (sec), leaf count = 127 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) = \left ( 6\,{\it \_f}-1 \right ) \left ( {\it \_g} \left ( { \it \_f} \right ) \right ) ^{3}+{\frac { \left ( 7\,{\it \_f}-1 \right ) \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}}{{\it \_f}}}+ {\frac {{\it \_g} \left ( {\it \_f} \right ) }{{\it \_f}}} \right \} , \left \{ {\it \_f}={\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ \left ( y \left ( x \right ) \right ) ^{2}}},{\it \_g} \left ( {\it \_f} \right ) =-{ \left ( y \left ( x \right ) \right ) ^{2} \left ( -{\frac { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) }{{\frac {\rm d}{{\rm d} x}}y \left ( x \right ) }}+2\,{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{-1}} \right \} , \left \{ x=\int \!{\frac {{\it \_g} \left ( {\it \_f} \right ) }{{\it \_f}\,{{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}}}}\,{\rm d}{ \it \_f}+{\it \_C1},y \left ( x \right ) ={{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}} \right \} ] \right ) \right \} \]