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′=dydx,y′′=d2ydx2), then which of the following statements is (are) true ?

Consider the family of all circles whose centers lie on the straight l

1.	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′=dydx,y′′=d2ydx2), then which of the following statements is (are) true ?
Answer» 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 $P y^{''} + Q y^{'} + 1 = 0$ , where $P, Q$ are functions of $x, y and y^{'} (here y^{'} = \frac{d y}{d x}, y^{''} = \frac{d^{2} y}{d x^{2}}),$ then which of the following statements is (are) true ?