ODE
\[ x \left (x^2+1\right ) y''(x)-2 \left (x^2+1\right ) y'(x)+2 x y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.184142 (sec), leaf count = 32
\[\left \{\left \{y(x)\to c_1 \left (x^2+1\right )+\frac {1}{2} c_2 \left (\left (x^2+1\right ) \tan ^{-1}(x)-x\right )\right \}\right \}\]
Maple ✓
cpu = 0.045 (sec), leaf count = 29
\[\left [y \left (x \right ) = \left (\left (-\frac {x}{2 \left (x^{2}+1\right )}+\frac {\arctan \left (x \right )}{2}\right ) \textit {\_C1} +\textit {\_C2} \right ) \left (x^{2}+1\right )\right ]\] Mathematica raw input
DSolve[2*x*y[x] - 2*(1 + x^2)*y'[x] + x*(1 + x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (1 + x^2)*C[1] + ((-x + (1 + x^2)*ArcTan[x])*C[2])/2}}
Maple raw input
dsolve(x*(x^2+1)*diff(diff(y(x),x),x)-2*(x^2+1)*diff(y(x),x)+2*x*y(x) = 0, y(x))
Maple raw output
[y(x) = ((-1/2*x/(x^2+1)+1/2*arctan(x))*_C1+_C2)*(x^2+1)]