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 = 1.83105 (sec), leaf count = 179

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

Maple
cpu = 0.024 (sec), leaf count = 71

\[ \left \{ {\frac {1}{-5-y \relax (x ) +2\,x} \left (\left (-5-y \relax (x ) +2\,x \right ) \ln \left ({\frac {-5-y \relax (x ) +2\,x}{x-2}} \right ) + \left (-5-y \relax (x ) +2\,x \right ) \ln \left (x-2 \right ) +{\it \_C1}\,y \relax (x ) + \left (-2\,{\it \_C1}+1 \right ) x+5\,{\it \_C1}-2 \right ) }=0 \right \} \] 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),'implicit')

Maple raw output

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