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

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 = 0.0236234 (sec), leaf count = 23

\[\left \{\left \{y(x)\to \frac {1}{e^{c_1} \sqrt {x^2+1}+1}\right \}\right \}\]

Maple
cpu = 0.009 (sec), leaf count = 19

\[ \left \{ -\sqrt {{x}^{2}+1}{\it \_C1}+ \left (y \relax (x ) \right ) ^{-1}-1=0 \right \} \] 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),'implicit')

Maple raw output

-(x^2+1)^(1/2)*_C1+1/y(x)-1 = 0