ODE
\[ y'(x)^3-y(x) y'(x)-x=0 \] ODE Classification
[_dAlembert]
Book solution method
Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)
Mathematica ✓
cpu = 185.849 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 52
\[ \left \{ [x \left ( {\it \_T} \right ) ={{\it \_T} \left ( 2\,\sqrt {{{\it \_T}}^{2}+1}+{\it \_C1} \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}},y \left ( {\it \_T} \right ) =-{1 \left ( 2\,\sqrt {{{\it \_T}}^{2}+1}+{\it \_C1} \right ) {\frac {1}{\sqrt {{{\it \_T}}^{2}+1}}}}+{{\it \_T}}^{2}] \right \} \] Mathematica raw input
DSolve[-x - y[x]*y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^3-y(x)*diff(y(x),x)-x = 0, y(x),'implicit')
Maple raw output
[x(_T) = 1/(_T^2+1)^(1/2)*_T*(2*(_T^2+1)^(1/2)+_C1), y(_T) = -1/(_T^2+1)^(1/2)*(2*(_T^2+1)^(1/2)+_C1)+_T^2]