ODE
\[ \left (x^2+1\right )^2 y''(x)+2 x \left (x^2+1\right ) y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.168376 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \frac {c_2 x+c_1}{\sqrt {x^2+1}}\right \}\right \}\]
Maple ✓
cpu = 0.059 (sec), leaf count = 24
\[\left [y \left (x \right ) = \frac {\textit {\_C1} x}{\sqrt {x^{2}+1}}+\frac {\textit {\_C2}}{\sqrt {x^{2}+1}}\right ]\] Mathematica raw input
DSolve[y[x] + 2*x*(1 + x^2)*y'[x] + (1 + x^2)^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + x*C[2])/Sqrt[1 + x^2]}}
Maple raw input
dsolve((x^2+1)^2*diff(diff(y(x),x),x)+2*x*(x^2+1)*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x/(x^2+1)^(1/2)+_C2/(x^2+1)^(1/2)]