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