4.1.47 \(y'(x)=x \left (x^3+2\right )-\left (2 x^2-y(x)\right ) y(x)\)

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

\[ \left \{ \left ({x}^{2}-y \relax (x ) \right ) ^{-1}-x-{\it \_C1}=0 \right \} \] 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