ODE
\[ x^2 y'(x)^3-2 x y(x) y'(x)^2+y(x)^2 y'(x)+1=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, \(f(y-x y', y')=0\)
Mathematica ✗
cpu = 599.997 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.05 (sec), leaf count = 37
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{3}+{\frac {27\,x}{4}}=0,y \left ( x \right ) ={\it \_C1}\,x-{\frac {1}{\sqrt {-{\it \_C1}}}},y \left ( x \right ) ={\it \_C1}\,x+{\frac {1}{\sqrt {-{\it \_C1}}}} \right \} \] Mathematica raw input
DSolve[1 + y[x]^2*y'[x] - 2*x*y[x]*y'[x]^2 + x^2*y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(x^2*diff(y(x),x)^3-2*x*y(x)*diff(y(x),x)^2+y(x)^2*diff(y(x),x)+1 = 0, y(x),'implicit')
Maple raw output
y(x)^3+27/4*x = 0, y(x) = _C1*x-1/(-_C1)^(1/2), y(x) = _C1*x+1/(-_C1)^(1/2)