Consider the family of all circles whose centres lie on the straight line y=x, If this family of circles is represented by the differential equation Py"+Qy'+1=0 , where P,Q are the functions of x, y and y' (here, y'=\frac{dy}{dx},y''=\frac{d^{2}y}{dx^{2}}), then which of the following statement (s) is /are true?