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 = 0.856277 (sec), leaf count = 22
\[\left \{\left \{y(x)\to 1+\frac {1}{c_2 x^2-c_1 x-1}\right \}\right \}\]
Maple ✓
cpu = 0.341 (sec), leaf count = 26
\[\left [y \left (x \right ) = \frac {x \left (\textit {\_C1} x -\textit {\_C2} \right )}{x^{2} \textit {\_C1} -\textit {\_C2} x -1}\right ]\] 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))
Maple raw output
[y(x) = x*(_C1*x-_C2)/(_C1*x^2-_C2*x-1)]