4.10.24 \((6 x-2 y(x)) y'(x)=-y(x)+3 x+2\)

ODE
\[ (6 x-2 y(x)) y'(x)=-y(x)+3 x+2 \] 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 = 0.0160503 (sec), leaf count = 29

\[\left \{\left \{y(x)\to 3 x-\frac {2}{5} \left (W\left (-e^{c_1+\frac {25 x}{4}-1}\right )+1\right )\right \}\right \}\]

Maple
cpu = 0.025 (sec), leaf count = 26

\[ \left \{ -{\frac {x}{5}}+{\frac {2\,y \relax (x ) }{5}}-{\frac {4\,\ln \left (5\,y \relax (x ) -15\,x+2 \right ) }{25}}-{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[(6*x - 2*y[x])*y'[x] == 2 + 3*x - y[x],y[x],x]

Mathematica raw output

{{y[x] -> 3*x - (2*(1 + ProductLog[-E^(-1 + (25*x)/4 + C[1])]))/5}}

Maple raw input

dsolve((6*x-2*y(x))*diff(y(x),x) = 2+3*x-y(x), y(x),'implicit')

Maple raw output

-1/5*x+2/5*y(x)-4/25*ln(5*y(x)-15*x+2)-_C1 = 0