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 = 0.0201164 (sec), leaf count = 58
\[\left \{\left \{y(x)\to -\frac {\sqrt {e^{2 c_1-x^2}+x^2}}{x}\right \},\left \{y(x)\to \frac {\sqrt {e^{2 c_1-x^2}+x^2}}{x}\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 21
\[ \left \{ -1-{\frac {{{\rm e}^{-{x}^{2}}}{\it \_C1}}{{x}^{2}}}+ \left ( y \left ( x \right ) \right ) ^{2}=0 \right \} \] 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),'implicit')
Maple raw output
-1-1/x^2*exp(-x^2)*_C1+y(x)^2 = 0