4.1672   x3 + (1− x2)xy′′(x)− y′(x) = 0

ODE

x3 + (1− x2) xy′′(x) − y′(x) = 0

ODE Classification

[[_2nd_order, _missing_y]]

Book solution method
TO DO

Mathematica
cpu = 0.0211616 (sec), leaf count = 30

{{                          } }
            ∘ -----2      x2
   y(x ) → − c1 1 − x + c2 + 2

Maple
cpu = 0.041 (sec), leaf count = 23

{                                 }
 y(x) = x2+ √ − 1-+x-√1-+x-C1 +-C2
        2

Mathematica raw input

DSolve[x^3 - y'[x] + x*(1 - x^2)*y''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x*(-x^2+1)*diff(diff(y(x),x),x)-diff(y(x),x)+x^3 = 0, y(x),'implicit')

Maple raw output

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