4.8.10 \(x \left (x^2+1\right ) y'(x)=\left (1-x^2\right ) y(x)\)

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 = 0.00857106 (sec), leaf count = 16

\[\left \{\left \{y(x)\to \frac {c_1 x}{x^2+1}\right \}\right \}\]

Maple
cpu = 0.013 (sec), leaf count = 14

\[ \left \{ y \relax (x ) ={\frac {{\it \_C1}\,x}{{x}^{2}+1}} \right \} \] 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),'implicit')

Maple raw output

y(x) = _C1*x/(x^2+1)