ODE
\[ x^2 y'(x)+x y(x) (x y(x)+4)+2=0 \] ODE Classification
[[_homogeneous, `class G`], _rational, _Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.250818 (sec), leaf count = 17
\[\left \{\left \{y(x)\to -\frac {2}{x}+\frac {1}{x+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.101 (sec), leaf count = 23
\[\left [y \left (x \right ) = -\frac {2 \textit {\_C1} -x}{x \left (-x +\textit {\_C1} \right )}\right ]\] Mathematica raw input
DSolve[2 + x*y[x]*(4 + x*y[x]) + x^2*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -2/x + (x + C[1])^(-1)}}
Maple raw input
dsolve(x^2*diff(y(x),x)+2+x*y(x)*(4+x*y(x)) = 0, y(x))
Maple raw output
[y(x) = -(2*_C1-x)/x/(-x+_C1)]