4.1.48 \(y'(x)=x \left (2-x^3\right )+\left (2 x^2-y(x)\right ) y(x)+1\)

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 = 0.0186806 (sec), leaf count = 25

\[\left \{\left \{y(x)\to -\frac {2}{2 c_1 e^{2 x}+1}+x^2+1\right \}\right \}\]

Maple
cpu = 0.033 (sec), leaf count = 32

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

Maple raw output

-ln(1-x^2+y(x))+ln(-x^2+y(x)-1)+2*x-_C1 = 0