4.1993   x2(1− y(x))y′′(x )+ 2x2y′(x)2 − 2x(1− y(x))y′(x )+ 2(1 − y(x))2y(x ) = 0

ODE

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

ODE Classification

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

Book solution method
TO DO

Mathematica
cpu = 0.793437 (sec), leaf count = 22

{{                       }}
         ------1-----
  y(x) → c2x2 − c1x− 1 + 1

Maple
cpu = 0.051 (sec), leaf count = 34

{(               )                      }
 -C1x2--−-C2x-−-1-y-(x)-−-C1x2-+--C2x
               y (x)− 1               = 0

Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

((_C1*x^2-_C2*x-1)*y(x)-_C1*x^2+_C2*x)/(y(x)-1) = 0