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]