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 = 0.173913 (sec), leaf count = 21
\[\left \{\left \{y(x)\to c_2 x-c_1 (x-i)^2\right \}\right \}\]
Maple ✓
cpu = 0.05 (sec), leaf count = 15
\[[y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} \left (x^{2}-1\right )]\] 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 + x)^2*C[1]) + x*C[2]}}
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*(x^2-1)]