##### 4.8.32 $$x \left (1-x^4\right ) y'(x)=\left (1-x^4\right ) y(x)+2 x \left (x^2-y(x)^2\right )$$

ODE
$x \left (1-x^4\right ) y'(x)=\left (1-x^4\right ) y(x)+2 x \left (x^2-y(x)^2\right )$ ODE Classiﬁcation

[[_homogeneous, class D], _rational, _Riccati]

Book solution method
Change of Variable, new dependent variable

Mathematica
cpu = 0.300637 (sec), leaf count = 46

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

Maple
cpu = 0.025 (sec), leaf count = 32

$\left [y \left (x \right ) = -\tanh \left (\frac {\ln \left (1+x \right )}{2}+\frac {\ln \left (x -1\right )}{2}-\frac {\ln \left (x^{2}+1\right )}{2}+2 \textit {\_C1} \right ) x\right ]$ Mathematica raw input

DSolve[x*(1 - x^4)*y'[x] == (1 - x^4)*y[x] + 2*x*(x^2 - y[x]^2),y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x*(-x^4+1)*diff(y(x),x) = 2*x*(x^2-y(x)^2)+(-x^4+1)*y(x), y(x))

Maple raw output

[y(x) = -tanh(1/2*ln(1+x)+1/2*ln(x-1)-1/2*ln(x^2+1)+2*_C1)*x]