Consider the family of all circles whose centers lie on the straight line `y=x`. If the 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^(')=(dy)/(dx),y^('')=(d^(2)y)/(dx^(2))`, then which of the following statements is (are) true?

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^(prime)+1=0, where P ,Q are functions of x , y and y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)), then which of the following statements is (are) true? (a) ( b ) (c) P=y+x (d) (e) (b) ( f ) (g) P=y-x (h) (i) (c) ( d ) (e) P+Q=1-x+y+y +( f ) (g)(( h ) (i) y^(( j )prime( k ))( l ) ( m ))^(( n )2( o ))( p ) (q) (r) (s) ( t ) (u) P-Q=x+y-y -( v ) (w)(( x ) (y) y^(( z )prime( a a ))( b b ) ( c c ))^(( d d )2( e e ))( f f ) (gg) (hh)

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