\[ x^2 (y(x)-1) y''(x)-2 x^2 y'(x)^2-2 x (y(x)-1) y'(x)-2 (y(x)-1)^2 y(x)=0 \] ✓ Mathematica : cpu = 0.671995 (sec), leaf count = 28
DSolve[-2*(-1 + y[x])^2*y[x] - 2*x*(-1 + y[x])*Derivative[1][y][x] - 2*x^2*Derivative[1][y][x]^2 + x^2*(-1 + y[x])*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to 1+\frac {1}{x^2 \left (-\frac {1}{x^2}-\frac {c_1}{x}+c_2\right )}\right \}\right \}\] ✓ Maple : cpu = 0.939 (sec), leaf count = 26
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))
\[y \left (x \right ) = \frac {x \left (c_{1} x -c_{2}\right )}{c_{1} x^{2}-x c_{2}-1}\]