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 = 0.153127 (sec), leaf count = 17
\[\{\{y(x)\to c_1 (x+(-1+c_1) c_1)\}\}\]
Maple ✓
cpu = 0.048 (sec), leaf count = 70
\[\left [y \left (x \right ) = \frac {x}{3}-\frac {2}{27}-\frac {2 \sqrt {-27 x^{3}+27 x^{2}-9 x +1}}{27}, y \left (x \right ) = \frac {x}{3}-\frac {2}{27}+\frac {2 \sqrt {-27 x^{3}+27 x^{2}-9 x +1}}{27}, y \left (x \right ) = \textit {\_C1}^{3}-\textit {\_C1}^{2}+x \textit {\_C1}\right ]\] 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))
Maple raw output
[y(x) = 1/3*x-2/27-2/27*(-27*x^3+27*x^2-9*x+1)^(1/2), y(x) = 1/3*x-2/27+2/27*(-27*x^3+27*x^2-9*x+1)^(1/2), y(x) = _C1^3-_C1^2+_C1*x]