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