4.15.49 $y^{\prime }(x)(-\log (y(x))-2x+1)+2y(x)=0$

ODE
$$y^{\prime }(x)(-\log (y(x))-2x+1)+2y(x)=0$$ ODE Classification

[[_1st_order, _with_linear_symmetries]]

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 0.0260441 (sec), leaf count = 23

$$\left\{\{y(x)\to -\frac{W(-2c_1{e}^{-2x})}{2c_1}\}\right\}$$

Maple ✓
cpu = 0.009 (sec), leaf count = 15

$$\{x+\frac{\ln \left(y\left(x\right)\right)}{2}-y\left(x\right)\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[2*y[x] + (1 - 2*x - Log[y[x]])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -ProductLog[(-2*C[1])/E^(2*x)]/(2*C[1])}}

Maple raw input

dsolve((1-2*x-ln(y(x)))*diff(y(x),x)+2*y(x) = 0, y(x),'implicit')

Maple raw output

x+1/2*ln(y(x))-y(x)*_C1 = 0