\[ -45 y^{(4)}(x) y^{(3)}(x) y''(x)+9 y^{(5)}(x) y''(x)^2+40 y^{(3)}(x)^3=0 \] ✗ Mathematica : cpu = 0.065138 (sec), leaf count = 0 , could not solve
DSolve[40*Derivative[3][y][x]^3 - 45*Derivative[2][y][x]*Derivative[3][y][x]*Derivative[4][y][x] + 9*Derivative[2][y][x]^2*Derivative[5][y][x] == 0, y[x], x]
✓ Maple : cpu = 3.56 (sec), leaf count = 110
\[ \left \{ y \left ( x \right ) =\int \!\!\!\int \!{\it RootOf} \left ( -\int ^{{\it \_Z}}\! \left ( {\it RootOf} \left ( -20\,\ln \left ( {\it \_f} \right ) +\int ^{{\it \_Z}}\!{\it \_k}\, \left ( {{\rm e}^{{\it RootOf} \left ( 81\,{{\it \_k}}^{2}{{\rm e}^{{\it \_Z}}}+20\,{{\rm e}^{{\it \_Z}}}\ln \left ( {{\rm e}^{{\it \_Z}}}+27 \right ) -40\,{{\rm e}^{{\it \_Z}}}\ln \left ( 2 \right ) -20\,{{\rm e}^{{\it \_Z}}}\ln \left ( 5 \right ) +162\,{{\rm e}^{{\it \_Z}}}{\it \_C1}-20\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+2187\,{{\it \_k}}^{2}+540\,\ln \left ( {{\rm e}^{{\it \_Z}}}+27 \right ) -1080\,\ln \left ( 2 \right ) -540\,\ln \left ( 5 \right ) +4374\,{\it \_C1}-540\,{\it \_Z}-540 \right ) }}+27 \right ) {d{\it \_k}}+20\,{\it \_C2} \right ) \right ) ^{-1}{d{\it \_f}}+x+{\it \_C3} \right ) \,{\rm d}x\,{\rm d}x+{\it \_C4}\,x+{\it \_C5} \right \} \]