4.31.38 \(\left (x^2+1\right ) y''(x)-2 x y'(x)+2 y(x)=0\)

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 = 0.447214 (sec), leaf count = 21

\[\left \{\left \{y(x)\to c_2 x-c_1 (x-i)^2\right \}\right \}\]

Maple
cpu = 0.016 (sec), leaf count = 16

\[ \left \{ y \left ( x \right ) ={\it \_C2}\,{x}^{2}+{\it \_C1}\,x-{\it \_C2} \right \} \] 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),'implicit')

Maple raw output

y(x) = _C2*x^2+_C1*x-_C2