ODE
\[ 2 y'(x)^2-(1-x) y'(x)-y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.163152 (sec), leaf count = 15
\[\{\{y(x)\to c_1 (x-1+2 c_1)\}\}\]
Maple ✓
cpu = 0.024 (sec), leaf count = 29
\[\left [y \left (x \right ) = -\frac {1}{8} x^{2}+\frac {1}{4} x -\frac {1}{8}, y \left (x \right ) = 2 \textit {\_C1}^{2}+x \textit {\_C1} -\textit {\_C1}\right ]\] Mathematica raw input
DSolve[-y[x] - (1 - x)*y'[x] + 2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*(-1 + x + 2*C[1])}}
Maple raw input
dsolve(2*diff(y(x),x)^2-(1-x)*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = -1/8*x^2+1/4*x-1/8, y(x) = 2*_C1^2+_C1*x-_C1]