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 = 0.0025685 (sec), leaf count = 17
\[\left \{\left \{y(x)\to c_1 (x-2)+c_1^2+1\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 24
\[ \left \{ y \left ( x \right ) =-{\frac {{x}^{2}}{4}}+x,y \left ( x \right ) =1+{{\it \_C1}}^{2}+ \left ( x-2 \right ) {\it \_C1} \right \} \] 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),'implicit')
Maple raw output
y(x) = -1/4*x^2+x, y(x) = 1+_C1^2+(x-2)*_C1