ODE
\[ -45 y''(x) y'''(x) y''''(x)+9 y''(x)^2 y'''''(x)+40 \left (y'''(x)\right )^3=0 \] ODE Classification
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.0723137 (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 = 0.479 (sec), leaf count = 105
\[ \left \{ y \left ( x \right ) =\int \!\!\!\int \!{\it RootOf} \left ( -\int ^{{\it \_Z}}\!{1 \left ( {\it RootOf} \left ( -\ln \left ( {\it \_f} \right ) -6\,\int ^{{\it \_Z}}\!{\frac {{\it \_k}}{\sqrt {{{\it \_k}}^{4}-{\it \_C1}}}}{d{\it \_k}}+{\it \_C2} \right ) \right ) ^{-1}{{\it \_f}}^{-{\frac {3}{2}}}}{d{\it \_f}}+x+{\it \_C3} \right ) \,{\rm d}x\,{\rm d}x+{\it \_C4}\,x+{\it \_C5},y \left ( x \right ) =\int \!\!\!\int \!{\it RootOf} \left ( -\int ^{{\it \_Z}}\!{1 \left ( {\it RootOf} \left ( -\ln \left ( {\it \_f} \right ) +6\,\int ^{{\it \_Z}}\!{\frac {{\it \_k}}{\sqrt {{{\it \_k}}^{4}-{\it \_C1}}}}{d{\it \_k}}+{\it \_C2} \right ) \right ) ^{-1}{{\it \_f}}^{-{\frac {3}{2}}}}{d{\it \_f}}+x+{\it \_C3} \right ) \,{\rm d}x\,{\rm d}x+{\it \_C4}\,x+{\it \_C5} \right \} \] Mathematica raw input
DSolve[40*y'''[x]^3 - 45*y''[x]*y'''[x]*y''''[x] + 9*y''[x]^2*y'''''[x] == 0,y[x],x]
Mathematica raw output
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 raw input
dsolve(9*diff(diff(y(x),x),x)^2*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-45*diff(diff(y(x),x),x)*diff(diff(diff(y(x),x),x),x)*diff(diff(diff(diff(y(x),x),x),x),x)+40*diff(diff(diff(y(x),x),x),x)^3 = 0, y(x),'implicit')
Maple raw output
y(x) = Int(Int(RootOf(-Intat(1/RootOf(-ln(_f)-6*Intat(1/(_k^4-_C1)^(1/2)*_k,_k = _Z)+_C2)/_f^(3/2),_f = _Z)+x+_C3),x),x)+_C4*x+_C5, y(x) = Int(Int(RootOf(-Intat(1/RootOf(-ln(_f)+6*Intat(1/(_k^4-_C1)^(1/2)*_k,_k = _Z)+_C2)/_f^(3/2),_f = _Z)+x+_C3),x),x)+_C4*x+_C5