ODE
\[ a x y'(x)-a y(x)+y'(x)^3=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✗
cpu = 600.017 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.021 (sec), leaf count = 28
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}+{\frac {4\,a{x}^{3}}{27}}=0,y \left ( x \right ) ={\it \_C1}\,x+{\frac {{{\it \_C1}}^{3}}{a}} \right \} \] Mathematica raw input
DSolve[-(a*y[x]) + a*x*y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^3+a*x*diff(y(x),x)-a*y(x) = 0, y(x),'implicit')
Maple raw output
y(x)^2+4/27*a*x^3 = 0, y(x) = _C1*x+_C1^3/a