4.1723   (1− x2)x2y′′(x)− (2− x2)xy′(x)+ (2− x2)y(x) = 0

ODE

(1− x2)x2y′′(x)− (2− x2)xy′(x)+ (2− x2)y(x) = 0

ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.0587328 (sec), leaf count = 45

{{                                      } }
         x 4√x2-− 1-(c2 log(√x2-−-1+ x) + c1)
   y(x) → ------------√4----2------------
                       1− x

Maple
cpu = 0.041 (sec), leaf count = 20

{        (   (   ∘ -2---)         )}
  y(x) = x ln  x+   x − 1  C2 + -C1

Mathematica raw input

DSolve[(2 - x^2)*y[x] - x*(2 - x^2)*y'[x] + x^2*(1 - x^2)*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (x*(-1 + x^2)^(1/4)*(C[1] + C[2]*Log[x + Sqrt[-1 + x^2]]))/(1 - x^2)^(
1/4)}}

Maple raw input

dsolve(x^2*(-x^2+1)*diff(diff(y(x),x),x)-x*(-x^2+2)*diff(y(x),x)+(-x^2+2)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = x*(ln(x+(x^2-1)^(1/2))*_C2+_C1)