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