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 = 0.172014 (sec), leaf count = 77
\[\left \{\left \{y(x)\to \frac {1}{12} \left (-i \sqrt {-x^2-8 x-16 (4+9 c_1)}+5 x+8\right )\right \},\left \{y(x)\to \frac {1}{12} \left (i \sqrt {-x^2-8 x-16 (4+9 c_1)}+5 x+8\right )\right \}\right \}\]
Maple ✓
cpu = 0.189 (sec), leaf count = 33
\[\left [y \left (x \right ) = -1-\frac {-\frac {5 \left (4+x \right ) \textit {\_C1}}{12}+\frac {\sqrt {\left (4+x \right )^{2} \textit {\_C1}^{2}+24}}{12}}{\textit {\_C1}}\right ]\] 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))
Maple raw output
[y(x) = -1-(-5/12*(4+x)*_C1+1/12*((4+x)^2*_C1^2+24)^(1/2))/_C1]