4.18.17 $x{y}^{\prime }(x{)}^2-(3x-y(x))y^{\prime }(x)+y(x)=0$

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

[[_homogeneous, `class A`], _dAlembert]

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

Mathematica ✗
cpu = 604.473 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 0.043 (sec), leaf count = 29

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

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

Mathematica raw output

$Aborted

Maple raw input

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

Maple raw output

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