ODE
\[ (4 y(x)+2 x+3) y'(x)=2 y(x)+x+1 \] 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 = 0.176688 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {1}{8} \left (W\left (-e^{8 x-1+c_1}\right )-4 x-5\right )\right \}\right \}\]
Maple ✓
cpu = 0.083 (sec), leaf count = 20
\[\left [y \left (x \right ) = -\frac {x}{2}+\frac {\LambertW \left ({\mathrm e}^{5} {\mathrm e}^{8 x} \textit {\_C1} \right )}{8}-\frac {5}{8}\right ]\] Mathematica raw input
DSolve[(3 + 2*x + 4*y[x])*y'[x] == 1 + x + 2*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (-5 - 4*x + ProductLog[-E^(-1 + 8*x + C[1])])/8}}
Maple raw input
dsolve((3+2*x+4*y(x))*diff(y(x),x) = 1+x+2*y(x), y(x))
Maple raw output
[y(x) = -1/2*x+1/8*LambertW(exp(5)*exp(x)^8*_C1)-5/8]