4.14.22 \(\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) (1-y(x))^2=0\)

ODE
\[ \left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) (1-y(x))^2=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0720819 (sec), leaf count = 30

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\log (\text {$\#$1})-\frac {2}{\text {$\#$1}-1}\& \right ]\left [c_1-\log \left (x^2+1\right )\right ]\right \}\right \}\]

Maple
cpu = 0.017 (sec), leaf count = 26

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

DSolve[2*x*(1 - y[x])^2*y[x] + (1 + x^2)*(1 + y[x]^2)*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> InverseFunction[Log[#1] - 2/(-1 + #1) & ][C[1] - Log[1 + x^2]]}}

Maple raw input

dsolve((x^2+1)*(1+y(x)^2)*diff(y(x),x)+2*x*y(x)*(1-y(x))^2 = 0, y(x),'implicit')

Maple raw output

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