ODE
\[ y'(x)=x \left (2-x^3\right )+\left (2 x^2-y(x)\right ) y(x)+1 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.221347 (sec), leaf count = 25
\[\left \{\left \{y(x)\to x^2-\frac {2}{1+2 c_1 e^{2 x}}+1\right \}\right \}\]
Maple ✓
cpu = 0.135 (sec), leaf count = 37
\[\left [y \left (x \right ) = \frac {x^{2} {\mathrm e}^{2 x} \textit {\_C1} -x^{2}+{\mathrm e}^{2 x} \textit {\_C1} +1}{{\mathrm e}^{2 x} \textit {\_C1} -1}\right ]\] Mathematica raw input
DSolve[y'[x] == 1 + x*(2 - x^3) + (2*x^2 - y[x])*y[x],y[x],x]
Mathematica raw output
{{y[x] -> 1 + x^2 - 2/(1 + 2*E^(2*x)*C[1])}}
Maple raw input
dsolve(diff(y(x),x) = 1+x*(-x^3+2)+(2*x^2-y(x))*y(x), y(x))
Maple raw output
[y(x) = (x^2*exp(x)^2*_C1-x^2+exp(x)^2*_C1+1)/(exp(x)^2*_C1-1)]