4.10.38 \((-4 y(x)+2 x+5) y'(x)=-2 y(x)+x+3\)

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

\[ \left \{ -{\it \_C1}+2\, \left (-x/2+y \relax (x ) \right ) ^{2}+3\,x-5\,y \relax (x ) =0 \right \} \] 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