ODE
\[ (-4 y(x)+2 x+5) y'(x)=-2 y(x)+x+3 \] 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 = 0.0106401 (sec), leaf count = 61
\[\left \{\left \{y(x)\to \frac {1}{4} \left (-i \sqrt {-16 c_1+4 x-25}+2 x+5\right )\right \},\left \{y(x)\to \frac {1}{4} \left (i \sqrt {-16 c_1+4 x-25}+2 x+5\right )\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 24
\[ \left \{ -{\it \_C1}+2\, \left ( -x/2+y \left ( x \right ) \right ) ^{2}+3\,x-5\,y \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[(5 + 2*x - 4*y[x])*y'[x] == 3 + x - 2*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (5 + 2*x - I*Sqrt[-25 + 4*x - 16*C[1]])/4}, {y[x] -> (5 + 2*x + I*Sqrt[-25 + 4*x - 16*C[1]])/4}}
Maple raw input
dsolve((5+2*x-4*y(x))*diff(y(x),x) = 3+x-2*y(x), y(x),'implicit')
Maple raw output
-_C1+2*(-1/2*x+y(x))^2+3*x-5*y(x) = 0