4.7.36 \((1-2 x) x y'(x)=y(x)^2-(4 x+1) y(x)+4 x\)

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 = 0.0137807 (sec), leaf count = 22

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

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

\[ \left \{ {\frac { \left (-x+{\it \_C1} \right ) y \relax (x ) +2\,{x}^{2}-{\it \_C1}}{y \relax (x ) -1}}=0 \right \} \] 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),'implicit')

Maple raw output

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