##### 4.13.41 $$x \left (1-y(x)^2\right ) y'(x)=\left (x^2+1\right ) y(x)$$

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.343598 (sec), leaf count = 57

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

Maple
cpu = 0.134 (sec), leaf count = 21

$\left [y \left (x \right ) = \frac {1}{\sqrt {-\frac {1}{\LambertW \left (-{\mathrm e}^{x^{2}} \textit {\_C1} \,x^{2}\right )}}}\right ]$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> (-I)*Sqrt[ProductLog[-(E^(x^2 - 2*C[1])*x^2)]]}, {y[x] -> I*Sqrt[Produ
ctLog[-(E^(x^2 - 2*C[1])*x^2)]]}}

Maple raw input

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

Maple raw output

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