ODE
\[ -4 y'(x) \left (y'''(x)\right )^2+3 y'(x) y''(x) y''''(x)-3 y''(x)^3=0 \] ODE Classification
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.100309 (sec), leaf count = 0 , could not solve
DSolve[-3*Derivative[2][y][x]^3 - 4*Derivative[1][y][x]*Derivative[3][y][x]^2 + 3*Derivative[1][y][x]*Derivative[2][y][x]*Derivative[4][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.854 (sec), leaf count = 142
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( \int \!{\frac {{\it \_j} \left ( {\it \_h} \right ) {{\rm e}^{\int \!{\it \_j} \left ( {\it \_h} \right ) \,{\rm d}{\it \_h}+{\it \_C2}}}}{{\it \_h}}}\,{\rm d}{\it \_h}+{\it \_C3},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_h}}}{\it \_j} \left ( {\it \_h} \right ) = \left ( -{\frac {{\it \_h}}{3}}-1 \right ) \left ( {\it \_j} \left ( {\it \_h} \right ) \right ) ^{3}+{\frac { \left ( {\it \_j} \left ( {\it \_h} \right ) \right ) ^{2}}{3}}-{\frac {{\it \_j} \left ( {\it \_h} \right ) }{3\,{\it \_h}}} \right \} , \left \{ {\it \_h}={\frac {{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) }{{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }},{\it \_j} \left ( {\it \_h} \right ) ={\frac { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) }{ \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) - \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) ^{2}}} \right \} , \left \{ x=\int \!{\frac {{\it \_j} \left ( {\it \_h} \right ) }{{\it \_h}}}\,{\rm d}{\it \_h}+{\it \_C1},y \left ( x \right ) =\int \!{\frac {{\it \_j} \left ( {\it \_h} \right ) {{\rm e}^{\int \!{\it \_j} \left ( {\it \_h} \right ) \,{\rm d}{\it \_h}+{\it \_C2}}}}{{\it \_h}}}\,{\rm d}{\it \_h}+{\it \_C3} \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[-3*y''[x]^3 - 4*y'[x]*y'''[x]^2 + 3*y'[x]*y''[x]*y''''[x] == 0,y[x],x]
Mathematica raw output
DSolve[-3*Derivative[2][y][x]^3 - 4*Derivative[1][y][x]*Derivative[3][y][x]^2 + 3*Derivative[1][y][x]*Derivative[2][y][x]*Derivative[4][y][x] == 0, y[x], x]
Maple raw input
dsolve(3*diff(y(x),x)*diff(diff(y(x),x),x)*diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(y(x),x)*diff(diff(diff(y(x),x),x),x)^2-3*diff(diff(y(x),x),x)^3 = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(Int(1/_h*_j(_h)*exp(Int(_j(_h),_h)+_C2),_h)+_C3,[{diff(_j(_h),_h) = (-1/3*_h-1)*_j(_h)^3+1/3*_j(_h)^2-1/3/_h*_j(_h)}, {_h = diff(diff(y(x),x),x)/diff(y(x),x), _j(_h) = diff(y(x),x)*diff(diff(y(x),x),x)/(diff(y(x),x)*diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)^2)}, {x = Int(1/_h*_j(_h),_h)+_C1, y(x) = Int(1/_h*_j(_h)*exp(Int(_j(_h),_h)+_C2),_h)+_C3}])