4.1522   (x2 + 1)y′′(x)− xy′(x) +y(x) = 0

ODE

(x2 + 1)y′′(x)− xy′(x)+ y(x) = 0

ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.0301513 (sec), leaf count = 29

{ {                                   }}
   y(x) → − c2∘x2-+-1+ c1x+ c2xsinh −1(x)

Maple
cpu = 0.038 (sec), leaf count = 23

{         ∘--2----      -               -  }
  y(x) = − x  + 1C2 + x (C2Arcsinh (x) + C1 )

Mathematica raw input

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

Mathematica raw output

{{y[x] -> x*C[1] - Sqrt[1 + x^2]*C[2] + x*ArcSinh[x]*C[2]}}

Maple raw input

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

Maple raw output

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