ODE
\[ x^2 (1-y(x)) y''(x)+2 x^2 y'(x)^2-2 x (1-y(x)) y'(x)+2 (1-y(x))^2 y(x)=0 \] 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
\[\left \{\left \{y(x)\to \frac {1}{c_2 x^2-c_1 x-1}+1\right \}\right \}\]
Maple ✓
cpu = 0.051 (sec), leaf count = 34
\[ \left \{ {\frac { \left ( {\it \_C1}\,{x}^{2}-{\it \_C2}\,x-1 \right ) y \left ( x \right ) -{\it \_C1}\,{x}^{2}+{\it \_C2}\,x}{y \left ( x \right ) -1}}=0 \right \} \] 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