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 = 0.0376377 (sec), leaf count = 46

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

Maple
cpu = 0.013 (sec), leaf count = 36

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

Maple raw output

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