ODE
\[ a+x y'(x)^3-y(x) y'(x)^2=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✗
cpu = 599.999 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.024 (sec), leaf count = 28
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{3}-{\frac {27\,a{x}^{2}}{4}}=0,y \left ( x \right ) ={\frac {{{\it \_C1}}^{3}x+a}{{{\it \_C1}}^{2}}} \right \} \] Mathematica raw input
DSolve[a - y[x]*y'[x]^2 + x*y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(x*diff(y(x),x)^3-y(x)*diff(y(x),x)^2+a = 0, y(x),'implicit')
Maple raw output
y(x)^3-27/4*a*x^2 = 0, y(x) = (_C1^3*x+a)/_C1^2