4.7.36 $(1-2x)x{y}^{\prime }(x)=y(x{)}^2-(4x+1)y(x)+4x$

ODE
$$(1-2x)x{y}^{\prime }(x)=y(x{)}^2-(4x+1)y(x)+4x$$ ODE Classification

[_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica ✓
cpu = 0.0137807 (sec), leaf count = 22

$$\left\{\{y(x)\to \frac{x(2x-1)}{x-c_1}+1\}\right\}$$

Maple ✓
cpu = 0.02 (sec), leaf count = 27

$$\{\frac{(-x+\mathit{\_}\mathit{C}\mathit{1})y\left(x\right)+2x^2-\mathit{\_}\mathit{C}\mathit{1}}{y\left(x\right)-1}=0\}$$ 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),'implicit')

Maple raw output

((-x+_C1)*y(x)+2*x^2-_C1)/(y(x)-1) = 0