4.10.5 \((y(x)-3 x+2) y'(x)-3 y(x)-2 x+5=0\)

ODE
\[ (y(x)-3 x+2) y'(x)-3 y(x)-2 x+5=0 \] 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 = 0.0118295 (sec), leaf count = 63

\[\left \{\left \{y(x)\to -i \sqrt {-c_1-11 x^2+22 x-4}+3 x-2\right \},\left \{y(x)\to i \sqrt {-c_1-11 x^2+22 x-4}+3 x-2\right \}\right \}\]

Maple
cpu = 0.02 (sec), leaf count = 44

\[ \left \{ -{\frac {1}{2}\ln \left ({\frac { \left (y \relax (x ) \right ) ^{2}+ \left (-6\,x+4 \right ) y \relax (x ) -2\,{x}^{2}+10\,x-7}{ \left (-1+x \right ) ^{2}}} \right ) }-\ln \left (-1+x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[5 - 2*x - 3*y[x] + (2 - 3*x + y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -2 + 3*x - I*Sqrt[-4 + 22*x - 11*x^2 - C[1]]}, {y[x] -> -2 + 3*x + I*S
qrt[-4 + 22*x - 11*x^2 - C[1]]}}

Maple raw input

dsolve((2-3*x+y(x))*diff(y(x),x)+5-2*x-3*y(x) = 0, y(x),'implicit')

Maple raw output

-1/2*ln((y(x)^2+(-6*x+4)*y(x)-2*x^2+10*x-7)/(-1+x)^2)-ln(-1+x)-_C1 = 0