4.22.9 $2y^{\prime }(x{)}^3+x{y}^{\prime }(x)-2y(x)=0$

ODE
$$2y^{\prime }(x{)}^3+x{y}^{\prime }(x)-2y(x)=0$$ 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 = 599.999 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 0.016 (sec), leaf count = 25

$$\{[x\left(\mathit{\_}\mathit{T}\right)=\mathit{\_}\mathit{T}(6\mathit{\_}\mathit{T}+\mathit{\_}\mathit{C}\mathit{1}),y\left(\mathit{\_}\mathit{T}\right)=\frac{{\mathit{\_}\mathit{T}}^2(8\mathit{\_}\mathit{T}+\mathit{\_}\mathit{C}\mathit{1})}{2}]\}$$ Mathematica raw input

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

Mathematica raw output

$Aborted

Maple raw input

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

Maple raw output

[x(_T) = _T*(6*_T+_C1), y(_T) = 1/2*_T^2*(8*_T+_C1)]