4.4.31 $$y(x) (a x y(x)+2)+b x+x y'(x)=0$$

ODE
$y(x) (a x y(x)+2)+b x+x y'(x)=0$ ODE Classiﬁcation

[_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica
cpu = 0.294358 (sec), leaf count = 43

$\left \{\left \{y(x)\to -\frac {1}{a x}-\sqrt {\frac {b}{a}} \tan \left (a x \sqrt {\frac {b}{a}}-c_1\right )\right \}\right \}$

Maple
cpu = 0.059 (sec), leaf count = 63

$\left [y \left (x \right ) = -\frac {-\frac {i \sqrt {a}\, \sqrt {b}\, x -1}{x}+\frac {{\mathrm e}^{-2 i \sqrt {a}\, \sqrt {b}\, x}}{\textit {\_C1} -\frac {i {\mathrm e}^{-2 i \sqrt {a}\, \sqrt {b}\, x}}{2 \sqrt {a}\, \sqrt {b}}}}{a}\right ]$ Mathematica raw input

DSolve[b*x + y[x]*(2 + a*x*y[x]) + x*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(1/(a*x)) - Sqrt[b/a]*Tan[a*Sqrt[b/a]*x - C[1]]}}

Maple raw input

dsolve(x*diff(y(x),x)+b*x+(2+a*x*y(x))*y(x) = 0, y(x))

Maple raw output

[y(x) = -(-(I*a^(1/2)*b^(1/2)*x-1)/x+exp(-2*I*a^(1/2)*b^(1/2)*x)/(_C1-1/2*I/a^(1
/2)/b^(1/2)*exp(-2*I*a^(1/2)*b^(1/2)*x)))/a]