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 = 0.176434 (sec), leaf count = 61
\[\left \{\left \{y(x)\to \frac {1}{4} \left (2 x-i \sqrt {4 x-25-16 c_1}+5\right )\right \},\left \{y(x)\to \frac {1}{4} \left (2 x+i \sqrt {4 x-25-16 c_1}+5\right )\right \}\right \}\]
Maple ✓
cpu = 0.029 (sec), leaf count = 41
\[\left [y \left (x \right ) = \frac {x}{2}+\frac {5}{4}-\frac {\sqrt {4 \textit {\_C1} -4 x +25}}{4}, y \left (x \right ) = \frac {x}{2}+\frac {5}{4}+\frac {\sqrt {4 \textit {\_C1} -4 x +25}}{4}\right ]\] 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))
Maple raw output
[y(x) = 1/2*x+5/4-1/4*(4*_C1-4*x+25)^(1/2), y(x) = 1/2*x+5/4+1/4*(4*_C1-4*x+25)^(1/2)]