4.10.3 \((-y(x)-2 x+5) y'(x)-2 y(x)-x+4=0\)

ODE
\[ (-y(x)-2 x+5) y'(x)-2 y(x)-x+4=0 \] 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 = 0.00993643 (sec), leaf count = 53

\[\left \{\left \{y(x)\to -\sqrt {c_1+3 x^2-12 x+25}-2 x+5\right \},\left \{y(x)\to \sqrt {c_1+3 x^2-12 x+25}-2 x+5\right \}\right \}\]

Maple
cpu = 0.02 (sec), leaf count = 42

\[ \left \{ -{\frac {1}{2}\ln \left ({\frac { \left (y \relax (x ) \right ) ^{2}+ \left (-10+4\,x \right ) y \relax (x ) +{x}^{2}-8\,x+13}{ \left (x-2 \right ) ^{2}}} \right ) }-\ln \left (x-2 \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[4 - x - 2*y[x] + (5 - 2*x - y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> 5 - 2*x - Sqrt[25 - 12*x + 3*x^2 + C[1]]}, {y[x] -> 5 - 2*x + Sqrt[25 
- 12*x + 3*x^2 + C[1]]}}

Maple raw input

dsolve((5-2*x-y(x))*diff(y(x),x)+4-x-2*y(x) = 0, y(x),'implicit')

Maple raw output

-1/2*ln((y(x)^2+(-10+4*x)*y(x)+x^2-8*x+13)/(x-2)^2)-ln(x-2)-_C1 = 0