Differential Equations

consider the family of all circles whose center 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 function of x,y‌and‌y′(here‌y′=

dy

dx

,y"=

d2y

dx2

),then which of the following statements is (are) true ?