4.10.37 \((4 y(x)+2 x+3) y'(x)=2 y(x)+x+1\)

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 = 0.0141727 (sec), leaf count = 26

\[\left \{\left \{y(x)\to \frac {1}{8} \left (W\left (-e^{c_1+8 x-1}\right )-4 x-5\right )\right \}\right \}\]

Maple
cpu = 0.031 (sec), leaf count = 26

\[ \left \{ {\frac {x}{2}}-{\frac {\ln \left (5+4\,x+8\,y \relax (x ) \right ) }{8}}-y \relax (x ) -{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

1/2*x-1/8*ln(5+4*x+8*y(x))-y(x)-_C1 = 0