ODE
\[ \left (x^2+1\right ) y'(x)+x (1-y(x)) y(x)=0 \] ODE Classification
[_separable]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.315082 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {1}{1+e^{c_1} \sqrt {x^2+1}}\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 17
\[\left [y \left (x \right ) = \frac {1}{1+\sqrt {x^{2}+1}\, \textit {\_C1}}\right ]\] Mathematica raw input
DSolve[x*(1 - y[x])*y[x] + (1 + x^2)*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (1 + E^C[1]*Sqrt[1 + x^2])^(-1)}}
Maple raw input
dsolve((x^2+1)*diff(y(x),x)+x*y(x)*(1-y(x)) = 0, y(x))
Maple raw output
[y(x) = 1/(1+(x^2+1)^(1/2)*_C1)]