Consider the family of all circles whose centers 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 functions of x, y and y' (here $$y' = \frac{dy}{dx}, y'' = \frac{d^2y}{dx^2}$$), then which of the following statements is (are) true?

A

P = y + x .

B

P = y - x

C

$$P + Q = 1 - x + y + y' + (y')^2$$

D

$$P - Q = x + y - y'- (y')^2$$