##### 4.11.17 $$x y(x) y'(x)=\left (x^2+1\right ) \left (1-y(x)^2\right )$$

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.303072 (sec), leaf count = 58

$\left \{\left \{y(x)\to -\frac {\sqrt {x^2+e^{-x^2+2 c_1}}}{x}\right \},\left \{y(x)\to \frac {\sqrt {x^2+e^{-x^2+2 c_1}}}{x}\right \}\right \}$

Maple
cpu = 0.032 (sec), leaf count = 44

$\left [y \left (x \right ) = \frac {\sqrt {{\mathrm e}^{-x^{2}} \textit {\_C1} +x^{2}}}{x}, y \left (x \right ) = -\frac {\sqrt {{\mathrm e}^{-x^{2}} \textit {\_C1} +x^{2}}}{x}\right ]$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> -(Sqrt[E^(-x^2 + 2*C[1]) + x^2]/x)}, {y[x] -> Sqrt[E^(-x^2 + 2*C[1]) +
 x^2]/x}}

Maple raw input

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

Maple raw output

[y(x) = (exp(-x^2)*_C1+x^2)^(1/2)/x, y(x) = -(exp(-x^2)*_C1+x^2)^(1/2)/x]