4.22.18 $2x{y}^{\prime }(x{)}^3-3y(x)y^{\prime }(x{)}^2-x=0$

ODE
$$2x{y}^{\prime }(x{)}^3-3y(x)y^{\prime }(x{)}^2-x=0$$ ODE Classification

[[_1st_order, _with_linear_symmetries], _dAlembert]

Book solution method
Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Mathematica ✗
cpu = 603.304 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 0.028 (sec), leaf count = 33

$$\{x^3+{\left(y\left(x\right)\right)}^3=0,[x\left(\mathit{\_}\mathit{T}\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{T}}^2,y\left(\mathit{\_}\mathit{T}\right)=\frac{2\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{T}}^3}{3}-\frac{\mathit{\_}\mathit{C}\mathit{1}}{3}]\}$$ Mathematica raw input

DSolve[-x - 3*y[x]*y'[x]^2 + 2*x*y'[x]^3 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(2*x*diff(y(x),x)^3-3*y(x)*diff(y(x),x)^2-x = 0, y(x),'implicit')

Maple raw output

x^3+y(x)^3 = 0, [x(_T) = _C1*_T^2, y(_T) = 2/3*_C1*_T^3-1/3*_C1]