4.6.17 \(x^2 y'(x)+x y(x) (x y(x)+4)+2=0\)

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

\[ \left \{ \ln \relax (x ) -{\it \_C1}-\ln \left (2+xy \relax (x ) \right ) +\ln \left (1+xy \relax (x ) \right ) =0 \right \} \] 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