ODE
\[ y'(x)^2-2 x y'(x)+2 y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.157623 (sec), leaf count = 18
\[\left \{\left \{y(x)\to c_1 x-\frac {c_1{}^2}{2}\right \}\right \}\]
Maple ✓
cpu = 0.024 (sec), leaf count = 21
\[\left [y \left (x \right ) = \frac {x^{2}}{2}, y \left (x \right ) = -\frac {1}{2} \textit {\_C1}^{2}+x \textit {\_C1}\right ]\] Mathematica raw input
DSolve[2*y[x] - 2*x*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] - C[1]^2/2}}
Maple raw input
dsolve(diff(y(x),x)^2-2*x*diff(y(x),x)+2*y(x) = 0, y(x))
Maple raw output
[y(x) = 1/2*x^2, y(x) = -1/2*_C1^2+x*_C1]