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

ODE
\[ x \left (1-x^3\right ) y'(x)=x^2+y(x) (1-2 x y(x)) \] ODE Classification

[_rational, _Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica
cpu = 0.166011 (sec), leaf count = 24

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

Maple
cpu = 0.683 (sec), leaf count = 18

\[ \left \{ y \relax (x ) ={\frac {x \left ({\it \_C1}+x \right ) }{{\it \_C1}\,{x}^{2}+1}} \right \} \] Mathematica raw input

DSolve[x*(1 - x^3)*y'[x] == x^2 + y[x]*(1 - 2*x*y[x]),y[x],x]

Mathematica raw output

{{y[x] -> (x*(1 + 2*x*C[1]))/(x^2 + 2*C[1])}}

Maple raw input

dsolve(x*(-x^3+1)*diff(y(x),x) = x^2+(1-2*x*y(x))*y(x), y(x),'implicit')

Maple raw output

y(x) = x*(_C1+x)/(_C1*x^2+1)