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 $P{y}^{"} + Q{y}^{\text{'}} + 1 = 0,$ where $P, Q$ are functions of $x, y \& y^{\text{'}}$ $\left( y^{\text{'}}= \frac{dy}{dx}, y^{"} = \frac{d^{2}y}{d{x}^2}\right)$ , then which of the following statements is (are) true ?