4.1687   (1 − x )x2y′′(x)− (x+ 1)xy′(x) +y(x) = 0

ODE

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

ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.0220989 (sec), leaf count = 21

{ {                       }}
            x(c2log(x)+-c1)
   y(x) → −     x − 1

Maple
cpu = 0.021 (sec), leaf count = 17

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

Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x) = x*(ln(x)*_C2+_C1)/(-1+x)