ODE
\[ x \left (x^2+1\right ) y'(x)=\left (1-x^2\right ) y(x) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.163228 (sec), leaf count = 16
\[\left \{\left \{y(x)\to \frac {c_1 x}{x^2+1}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 14
\[\left [y \left (x \right ) = \frac {\textit {\_C1} x}{x^{2}+1}\right ]\] Mathematica raw input
DSolve[x*(1 + x^2)*y'[x] == (1 - x^2)*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (x*C[1])/(1 + x^2)}}
Maple raw input
dsolve(x*(x^2+1)*diff(y(x),x) = (-x^2+1)*y(x), y(x))
Maple raw output
[y(x) = _C1*x/(x^2+1)]