4.10.34 \((-3 y(x)-2 x+5) y'(x)-3 y(x)-2 x+1=0\)

ODE
\[ (-3 y(x)-2 x+5) y'(x)-3 y(x)-2 x+1=0 \] 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 = 0.0161991 (sec), leaf count = 30

\[\left \{\left \{y(x)\to -4 W\left (-e^{c_1+\frac {x}{12}-1}\right )-\frac {2 x}{3}-\frac {7}{3}\right \}\right \}\]

Maple
cpu = 0.024 (sec), leaf count = 22

\[ \left \{ -{\it \_C1}+x-4\,\ln \left (3\,y \relax (x ) +2\,x+7 \right ) +y \relax (x ) =0 \right \} \] Mathematica raw input

DSolve[1 - 2*x - 3*y[x] + (5 - 2*x - 3*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -7/3 - (2*x)/3 - 4*ProductLog[-E^(-1 + x/12 + C[1])]}}

Maple raw input

dsolve((5-2*x-3*y(x))*diff(y(x),x)+1-2*x-3*y(x) = 0, y(x),'implicit')

Maple raw output

-_C1+x-4*ln(3*y(x)+2*x+7)+y(x) = 0