ODE
\[ 2 y'(x)^3+x y'(x)-2 y(x)=0 \] 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
\[ \left \{ [x \left ( {\it \_T} \right ) ={\it \_T}\, \left ( 6\,{\it \_T}+{\it \_C1} \right ) ,y \left ( {\it \_T} \right ) ={\frac {{{\it \_T}}^{2} \left ( 8\,{\it \_T}+{\it \_C1} \right ) }{2}}] \right \} \] 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)]