\[ \boxed { 9\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) ^{2}{\frac {{\rm d}^{5}}{{\rm d}{x}^{5}}}y \left ( x \right ) -45\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) \left ( {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) \right ) {\it d4y} \left ( x \right ) +40\,{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.074009 (sec), leaf count = 41 \[ \text {DSolve}\left [40 y^{(3)}(x)^3+9 y^{(5)}(x) y''(x)^2-45 y^{(4)}(x) y^{(3)}(x) y''(x)=0,y(x),x\right ] \]
Maple: cpu = 0.515 (sec), leaf count = 110 \[ \left \{ y \left ( x \right ) =\int \!\!\!\int \!{\it RootOf} \left ( - \int ^{{\it \_Z}}\! \left ( {\it RootOf} \left ( -20\,\ln \left ( {\it \_f} \right ) +\int ^{{\it \_Z}}\!{\it \_k}\, \left ( {{\rm e}^{{\it RootOf} \left ( 81\,{{\it \_k}}^{2}{{\rm e}^{{\it \_Z}}}+20\,{{\rm e}^{ {\it \_Z}}}\ln \left ( {{\rm e}^{{\it \_Z}}}+27 \right ) -40\,{{\rm e}^ {{\it \_Z}}}\ln \left ( 2 \right ) -20\,{{\rm e}^{{\it \_Z}}}\ln \left ( 5 \right ) +162\,{\it \_C1}\,{{\rm e}^{{\it \_Z}}}-20\,{\it \_Z }\,{{\rm e}^{{\it \_Z}}}+2187\,{{\it \_k}}^{2}+540\,\ln \left ( { {\rm e}^{{\it \_Z}}}+27 \right ) -1080\,\ln \left ( 2 \right ) -540\, \ln \left ( 5 \right ) +4374\,{\it \_C1}-540\,{\it \_Z}-540 \right ) }}+ 27 \right ) {d{\it \_k}}+20\,{\it \_C2} \right ) \right ) ^{-1}{d{\it \_f}}+x+{\it \_C3} \right ) \,{\rm d}x\,{\rm d}x+{\it \_C4}\,x+{\it \_C5} \right \} \]