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