4.10.49 \((-12 y(x)+5 x+8) y'(x)=-5 y(x)+2 x+3\)

ODE
\[ (-12 y(x)+5 x+8) y'(x)=-5 y(x)+2 x+3 \] ODE Classification

[[_homogeneous, `class C`], _exact, _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 = 0.010099 (sec), leaf count = 77

\[\left \{\left \{y(x)\to \frac {1}{12} \left (-i \sqrt {-16 \left (9 c_1+4\right )-x^2-8 x}+5 x+8\right )\right \},\left \{y(x)\to \frac {1}{12} \left (i \sqrt {-16 \left (9 c_1+4\right )-x^2-8 x}+5 x+8\right )\right \}\right \}\]

Maple
cpu = 0.023 (sec), leaf count = 36

\[ \left \{ -{\frac {1}{2}\ln \left ({\frac { \left (x-2\,y \relax (x ) +2 \right ) \left (1+x-3\,y \relax (x ) \right ) }{ \left (4+x \right ) ^{2}}} \right ) }-\ln \left (4+x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[(8 + 5*x - 12*y[x])*y'[x] == 3 + 2*x - 5*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (8 + 5*x - I*Sqrt[-8*x - x^2 - 16*(4 + 9*C[1])])/12}, {y[x] -> (8 + 5*
x + I*Sqrt[-8*x - x^2 - 16*(4 + 9*C[1])])/12}}

Maple raw input

dsolve((8+5*x-12*y(x))*diff(y(x),x) = 3+2*x-5*y(x), y(x),'implicit')

Maple raw output

-1/2*ln((x-2*y(x)+2)*(1+x-3*y(x))/(4+x)^2)-ln(4+x)-_C1 = 0