ODE
\[ 2 x y'(x)^3-3 y(x) y'(x)^2-x=0 \] 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
\[ \left \{ {x}^{3}+ \left ( y \left ( x \right ) \right ) ^{3}=0,[x \left ( {\it \_T} \right ) ={\it \_C1}\,{{\it \_T}}^{2},y \left ( {\it \_T} \right ) ={\frac {2\,{\it \_C1}\,{{\it \_T}}^{3}}{3}}-{\frac {{\it \_C1}}{3}}] \right \} \] 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]