4.10.19 \((2 y(x)+x+1) y'(x)-2 y(x)-x+1=0\)

ODE
\[ (2 y(x)+x+1) y'(x)-2 y(x)-x+1=0 \] 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 = 0.0163198 (sec), leaf count = 30

\[\left \{\left \{y(x)\to \frac {1}{6} \left (4 W\left (-e^{c_1+\frac {9 x}{4}-1}\right )-3 x+1\right )\right \}\right \}\]

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

\[ \left \{ {\frac {2\,x}{3}}-{\frac {4\,\ln \left (-1+3\,x+6\,y \relax (x ) \right ) }{9}}-{\frac {2\,y \relax (x ) }{3}}-{\it \_C1}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (1 - 3*x + 4*ProductLog[-E^(-1 + (9*x)/4 + C[1])])/6}}

Maple raw input

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

Maple raw output

2/3*x-4/9*ln(-1+3*x+6*y(x))-2/3*y(x)-_C1 = 0