##### 4.9.48 $$(y(x)-x+3) y'(x)=3 y(x)-4 x+11$$

ODE
$(y(x)-x+3) y'(x)=3 y(x)-4 x+11$ 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 = 2.66409 (sec), leaf count = 179

$\text {Solve}\left [\frac {(-2)^{2/3} \left (-2 x \log \left (\frac {3 (-2)^{2/3} (-y(x)+2 x-5)}{-y(x)+x-3}\right )+(2 x-5) \log \left (-\frac {3 (-2)^{2/3} (x-2)}{-y(x)+x-3}\right )+5 \log \left (\frac {3 (-2)^{2/3} (-y(x)+2 x-5)}{-y(x)+x-3}\right )+y(x) \left (-\log \left (-\frac {3 (-2)^{2/3} (x-2)}{-y(x)+x-3}\right )+\log \left (\frac {3 (-2)^{2/3} (-y(x)+2 x-5)}{-y(x)+x-3}\right )-1\right )+x-3\right )}{9 (-y(x)+2 x-5)}=\frac {1}{9} (-2)^{2/3} \log (x-2)+c_1,y(x)\right ]$

Maple
cpu = 0.132 (sec), leaf count = 30

$\left [y \left (x \right ) = -1+\frac {\left (x -2\right ) \left (2 \LambertW \left (-\textit {\_C1} \left (x -2\right )\right )+1\right )}{\LambertW \left (-\textit {\_C1} \left (x -2\right )\right )}\right ]$ Mathematica raw input

DSolve[(3 - x + y[x])*y'[x] == 11 - 4*x + 3*y[x],y[x],x]

Mathematica raw output

Solve[((-2)^(2/3)*(-3 + x + (-5 + 2*x)*Log[(-3*(-2)^(2/3)*(-2 + x))/(-3 + x - y[
x])] + 5*Log[(3*(-2)^(2/3)*(-5 + 2*x - y[x]))/(-3 + x - y[x])] - 2*x*Log[(3*(-2)
^(2/3)*(-5 + 2*x - y[x]))/(-3 + x - y[x])] + (-1 - Log[(-3*(-2)^(2/3)*(-2 + x))/
(-3 + x - y[x])] + Log[(3*(-2)^(2/3)*(-5 + 2*x - y[x]))/(-3 + x - y[x])])*y[x]))
/(9*(-5 + 2*x - y[x])) == C[1] + ((-2)^(2/3)*Log[-2 + x])/9, y[x]]

Maple raw input

dsolve((3-x+y(x))*diff(y(x),x) = 11-4*x+3*y(x), y(x))

Maple raw output

[y(x) = -1+(x-2)*(2*LambertW(-_C1*(x-2))+1)/LambertW(-_C1*(x-2))]