4.21.39 $y^{\prime }(x{)}^3-(y(x)+3)y^{\prime }(x)+x=0$

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

[_dAlembert]

Book solution method
No Missing Variables ODE, Solve for $x$

Mathematica ✓
cpu = 152.507 (sec), leaf count = 1

$$\mathrm{\$}\text{Aborted}$$

Maple ✓
cpu = 0.024 (sec), leaf count = 63

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

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

Mathematica raw output

$Aborted

Maple raw input

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

Maple raw output

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