ODE
\[ (-2 y(x)-4 x+1) y'(x)+y(x)+2 x=0 \] ODE Classification
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
Book solution method
Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)
Mathematica ✓
cpu = 0.172018 (sec), leaf count = 28
\[\left \{\left \{y(x)\to -\frac {1}{10} W\left (-e^{-25 x-1+c_1}\right )-2 x+\frac {2}{5}\right \}\right \}\]
Maple ✓
cpu = 0.103 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {{\mathrm e}^{-\LambertW \left (-2 \,{\mathrm e}^{4} {\mathrm e}^{-25 x} {\mathrm e}^{25 \textit {\_C1}}\right )+4-25 x +25 \textit {\_C1}}}{5}+\frac {2}{5}-2 x\right ]\] Mathematica raw input
DSolve[2*x + y[x] + (1 - 4*x - 2*y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> 2/5 - 2*x - ProductLog[-E^(-1 - 25*x + C[1])]/10}}
Maple raw input
dsolve((1-4*x-2*y(x))*diff(y(x),x)+2*x+y(x) = 0, y(x))
Maple raw output
[y(x) = 1/5*exp(-LambertW(-2*exp(4)/exp(x)^25*exp(_C1)^25)+4-25*x+25*_C1)+2/5-2*x]