ODE
\[ (1-2 x) x y'(x)=y(x)^2-(4 x+1) y(x)+4 x \] ODE Classification
[_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.27472 (sec), leaf count = 22
\[\left \{\left \{y(x)\to 1+\frac {x (2 x-1)}{x-c_1}\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {-2 x^{2}+\textit {\_C1}}{-x +\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[(1 - 2*x)*x*y'[x] == 4*x - (1 + 4*x)*y[x] + y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> 1 + (x*(-1 + 2*x))/(x - C[1])}}
Maple raw input
dsolve(x*(1-2*x)*diff(y(x),x) = 4*x-(1+4*x)*y(x)+y(x)^2, y(x))
Maple raw output
[y(x) = (-2*x^2+_C1)/(-x+_C1)]