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.