ODE
\[ (-2 y(x)+2 x+3) y'(x)=-2 y(x)+6 x+1 \] 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 = 0.00981036 (sec), leaf count = 67
\[\left \{\left \{y(x)\to -\frac {1}{2} i \sqrt {-4 c_1+8 x^2-8 x-9}+x+\frac {3}{2}\right \},\left \{y(x)\to \frac {1}{2} i \sqrt {-4 c_1+8 x^2-8 x-9}+x+\frac {3}{2}\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 50
\[ \left \{ -{\frac {1}{2}\ln \left ( {\frac {4\, \left ( y \left ( x \right ) \right ) ^{2}+ \left ( -8\,x-12 \right ) y \left ( x \right ) +12\,{x}^{2}+4\,x+11}{ \left ( -1+2\,x \right ) ^{2}}} \right ) }-\ln \left ( -1+2\,x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[(3 + 2*x - 2*y[x])*y'[x] == 1 + 6*x - 2*y[x],y[x],x]
Mathematica raw output
{{y[x] -> 3/2 + x - (I/2)*Sqrt[-9 - 8*x + 8*x^2 - 4*C[1]]}, {y[x] -> 3/2 + x + (I/2)*Sqrt[-9 - 8*x + 8*x^2 - 4*C[1]]}}
Maple raw input
dsolve((3+2*x-2*y(x))*diff(y(x),x) = 1+6*x-2*y(x), y(x),'implicit')
Maple raw output
-1/2*ln((4*y(x)^2+(-8*x-12)*y(x)+12*x^2+4*x+11)/(-1+2*x)^2)-ln(-1+2*x)-_C1 = 0