ODE
\[ y'(x) (-\log (y(x))-2 x+1)+2 y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.339755 (sec), leaf count = 23
\[\left \{\left \{y(x)\to -\frac {W\left (-2 c_1 e^{-2 x}\right )}{2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.078 (sec), leaf count = 19
\[[y \left (x \right ) = {\mathrm e}^{-\LambertW \left (-2 \,{\mathrm e}^{-2 x} \textit {\_C1} \right )-2 x}]\] Mathematica raw input
DSolve[2*y[x] + (1 - 2*x - Log[y[x]])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/2*ProductLog[(-2*C[1])/E^(2*x)]/C[1]}}
Maple raw input
dsolve((1-2*x-ln(y(x)))*diff(y(x),x)+2*y(x) = 0, y(x))
Maple raw output
[y(x) = exp(-LambertW(-2*exp(-2*x)*_C1)-2*x)]