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)

Options

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

Answer

B, C