ODE
\[ y'(x)^2-x y'(x)+y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.00232628 (sec), leaf count = 14
\[\left \{\left \{y(x)\to c_1 \left (x-c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( x-{\it \_C1} \right ) ,y \left ( x \right ) ={\frac {{x}^{2}}{4}} \right \} \] Mathematica raw input
DSolve[y[x] - x*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x - C[1])*C[1]}}
Maple raw input
dsolve(diff(y(x),x)^2-x*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = 1/4*x^2, y(x) = _C1*(x-_C1)