ODE No. 1770

\[ x^2 (y(x)-1) y''(x)-2 x^2 y'(x)^2-2 x (y(x)-1) y'(x)-2 (y(x)-1)^2 y(x)=0 \]

✓ Mathematica : cpu = 0.701536 (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 = 0.066 (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))

\[y \left (x \right ) = \frac {x \left (x c_{1} -c_{2} \right )}{c_{1} x^{2}-c_{2} x -1}\]