Differentiating w.r.t.x we have
2x-2+2y dy/dx-2dy/dx =0 So,x - 1+ydy/dx-dy/dx =0
So x-1+(y-1)dy/dx=0
dy/dx=1-x/y-1
differentiating again w.r.t.x,we get
1+(y-1)d²y/dx² +(dy/dx)^2=0
Now how to calculate required differential equation.
If my calculations of 1st and 2nd order derivative is wrong, reply me accordingly.