4.15.49 \(y'(x) (-\log (y(x))-2 x+1)+2 y(x)=0\)

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 = 0.0260441 (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 = 0.009 (sec), leaf count = 15

\[ \left \{ x+{\frac {\ln \left (y \relax (x ) \right ) }{2}}-y \relax (x ) {\it \_C1}=0 \right \} \] 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