4.10.23 \((-2 y(x)-4 x+1) y'(x)+y(x)+2 x=0\)

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 = 0.0291591 (sec), leaf count = 28

\[\left \{\left \{y(x)\to -\frac {1}{10} W\left (-e^{c_1-25 x-1}\right )-2 x+\frac {2}{5}\right \}\right \}\]

Maple
cpu = 0.026 (sec), leaf count = 26

\[ \left \{ {\frac {x}{5}}+{\frac {\ln \left (-2+10\,x+5\,y \relax (x ) \right ) }{25}}-{\frac {2\,y \relax (x ) }{5}}-{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

1/5*x+1/25*ln(-2+10*x+5*y(x))-2/5*y(x)-_C1 = 0