ODE
\[ y'(x)=x \left (x^3+2\right )-\left (2 x^2-y(x)\right ) y(x) \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.00691611 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \frac {1}{c_1-x}+x^2\right \}\right \}\]
Maple ✓
cpu = 0.027 (sec), leaf count = 20
\[ \left \{ \left ( {x}^{2}-y \left ( x \right ) \right ) ^{-1}-x-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[y'[x] == x*(2 + x^3) - (2*x^2 - y[x])*y[x],y[x],x]
Mathematica raw output
{{y[x] -> x^2 + (-x + C[1])^(-1)}}
Maple raw input
dsolve(diff(y(x),x) = x*(x^3+2)-(2*x^2-y(x))*y(x), y(x),'implicit')
Maple raw output
1/(x^2-y(x))-x-_C1 = 0