##### 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 = 0.434975 (sec), leaf count = 30

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

Maple
cpu = 0.199 (sec), leaf count = 40

$[y \left (x \right ) = {\mathrm e}^{\RootOf \left (\ln \left (x^{2}+1\right ) {\mathrm e}^{\textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} \textit {\_C1} +{\mathrm e}^{\textit {\_Z}} \textit {\_Z} -\ln \left (x^{2}+1\right )-2 \textit {\_C1} -\textit {\_Z} -2\right )}]$ 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))

Maple raw output

[y(x) = exp(RootOf(ln(x^2+1)*exp(_Z)+2*exp(_Z)*_C1+exp(_Z)*_Z-ln(x^2+1)-2*_C1-_Z
-2))]