ODE
\[ \left (x^2+1\right ) y''(x)+2 x y'(x)-2 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.157604 (sec), leaf count = 48
\[\left \{\left \{y(x)\to \frac {1}{2} i (2 c_1 x-c_2 x \log (1-i x)+c_2 x \log (1+i x)+2 i c_2)\right \}\right \}\]
Maple ✓
cpu = 0.061 (sec), leaf count = 16
\[[y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} \left (\arctan \left (x \right ) x +1\right )]\] Mathematica raw input
DSolve[-2*y[x] + 2*x*y'[x] + (1 + x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (I/2)*(2*x*C[1] + (2*I)*C[2] - x*C[2]*Log[1 - I*x] + x*C[2]*Log[1 + I*x])}}
Maple raw input
dsolve((x^2+1)*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x+_C2*(arctan(x)*x+1)]