ODE
\[ y'(x)^2-(2-x) y'(x)-y(x)+1=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.139755 (sec), leaf count = 17
\[\left \{\left \{y(x)\to c_1 (x-2)+1+c_1{}^2\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 25
\[\left [y \left (x \right ) = x -\frac {1}{4} x^{2}, y \left (x \right ) = \textit {\_C1}^{2}+x \textit {\_C1} -2 \textit {\_C1} +1\right ]\] Mathematica raw input
DSolve[1 - y[x] - (2 - x)*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> 1 + (-2 + x)*C[1] + C[1]^2}}
Maple raw input
dsolve(diff(y(x),x)^2-(2-x)*diff(y(x),x)+1-y(x) = 0, y(x))
Maple raw output
[y(x) = x-1/4*x^2, y(x) = _C1^2+_C1*x-2*_C1+1]