ODE
\[ y'(x)^3-y'(x)^2+x y'(x)-y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.00248597 (sec), leaf count = 17
\[\left \{\left \{y(x)\to c_1 \left (\left (c_1-1\right ) c_1+x\right )\right \}\right \}\]
Maple ✓
cpu = 0.039 (sec), leaf count = 40
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}+{\frac { \left ( -18\,x+4 \right ) y \left ( x \right ) }{27}}+{\frac {4\,{x}^{3}}{27}}-{\frac {{x}^{2}}{27}}=0,y \left ( x \right ) ={\it \_C1}\, \left ( {{\it \_C1}}^{2}-{\it \_C1}+x \right ) \right \} \] Mathematica raw input
DSolve[-y[x] + x*y'[x] - y'[x]^2 + y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*(x + (-1 + C[1])*C[1])}}
Maple raw input
dsolve(diff(y(x),x)^3-diff(y(x),x)^2+x*diff(y(x),x)-y(x) = 0, y(x),'implicit')
Maple raw output
y(x)^2+1/27*(-18*x+4)*y(x)+4/27*x^3-1/27*x^2 = 0, y(x) = _C1*(_C1^2-_C1+x)