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 = 0.00801237 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \frac {1}{c_1+x}-\frac {2}{x}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 25
\[ \left \{ \ln \left ( x \right ) -{\it \_C1}-\ln \left ( 2+xy \left ( x \right ) \right ) +\ln \left ( 1+xy \left ( x \right ) \right ) =0 \right \} \] 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),'implicit')
Maple raw output
ln(x)-_C1-ln(2+x*y(x))+ln(1+x*y(x)) = 0