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 = 0.228877 (sec), leaf count = 17
\[\left \{\left \{y(x)\to x^2+\frac {1}{-x+c_1}\right \}\right \}\]
Maple ✓
cpu = 0.04 (sec), leaf count = 20
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \,x^{2}+x^{3}-1}{x +\textit {\_C1}}\right ]\] 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))
Maple raw output
[y(x) = (_C1*x^2+x^3-1)/(x+_C1)]