\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) {\it d4y} \left ( x \right ) - \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) + \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.083511 (sec), leaf count = 37 \[ \text {DSolve}\left [y^{(4)}(x) y'(x)-y^{(3)}(x) y''(x)+y^{(3)}(x) y'(x)^3=0,y(x),x\right ] \]
Maple: cpu = 1.092 (sec), leaf count = 165 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( \int \!{\frac {{ \it \_j} \left ( {\it \_h} \right ) }{{{\rm e}^{\int \!{\it \_j} \left ( {\it \_h} \right ) \,{\rm d}{\it \_h}+{\it \_C2}}}{\it \_h}}}\,{\rm d}{ \it \_h}+{\it \_C3},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_h}}}{\it \_j} \left ( {\it \_h} \right ) = \left ( 12\,{\it \_h}+3 \right ) \left ( {\it \_j} \left ( {\it \_h} \right ) \right ) ^{3}+{\frac { \left ( 10\,{\it \_h}+1 \right ) \left ( {\it \_j} \left ( {\it \_h} \right ) \right ) ^{2}}{{\it \_h}}}+{\frac {{\it \_j} \left ( {\it \_h} \right ) }{{\it \_h}}} \right \} , \left \{ {\it \_h}={\frac {{\frac { {\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) }{ \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{3}}},{\it \_j} \left ( {\it \_h} \right ) =-{ \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{3} \left ( -{\frac { \left ( {\frac {\rm d}{{\rm d}x }}y \left ( x \right ) \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) }{{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) }}+3\,{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) ^{-1}} \right \} , \left \{ x=\int \!{\frac {{\it \_j} \left ( {\it \_h} \right ) }{{\it \_h}\, \left ( {{\rm e}^{\int \!{\it \_j} \left ( {\it \_h} \right ) \,{\rm d}{\it \_h}+{\it \_C2}}} \right ) ^{2}}}\,{\rm d}{\it \_h}+{\it \_C1},y \left ( x \right ) =\int \!{\frac {{\it \_j} \left ( {\it \_h} \right ) }{{{\rm e}^{\int \!{\it \_j} \left ( {\it \_h} \right ) \,{\rm d}{\it \_h}+{\it \_C2}}}{\it \_h}}} \,{\rm d}{\it \_h}+{\it \_C3} \right \} ] \right ) \right \} \]