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 = 0.0272619 (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 = 0.01 (sec), leaf count = 23

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

Maple raw output

1/2*x^2+ln(x)+1/2*y(x)^2-ln(y(x))+_C1 = 0