ODE
\[ y'(x)^3-2 x y'(x)-y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✗
cpu = 600. (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.041 (sec), leaf count = 31
\[ \left \{ [x \left ( {\it \_T} \right ) ={1 \left ( {\frac {3}{8}{{\it \_T}}^{{\frac {8}{3}}}}+{\it \_C1} \right ) {{\it \_T}}^{-{\frac {2}{3}}}},y \left ( {\it \_T} \right ) ={\frac {{{\it \_T}}^{3}}{4}}-2\,\sqrt [3]{{\it \_T}}{\it \_C1}] \right \} \] Mathematica raw input
DSolve[-y[x] - 2*x*y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^3-2*x*diff(y(x),x)-y(x) = 0, y(x),'implicit')
Maple raw output
[x(_T) = 1/_T^(2/3)*(3/8*_T^(8/3)+_C1), y(_T) = 1/4*_T^3-2*_T^(1/3)*_C1]