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^(primeprime)+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)`P=y+x` (b)`P=y-x` (c)`P+Q=1-x+y+y^(prime)+(y^(prime))^2` (d)`P-Q=x+y-y^(prime)-(y^(prime))^2`

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)

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 centres 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'=(dy)/(dx),y''=(d^(2)y)/(dx^(2)) ), then which of the following statements is (are) true?

If a function is represented parametrically be the equations x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t , then which of the following statements are true? y^(x-2x y^(prime))=y y y^(prime)=2x(y^(prime))^2+1 x y^(prime)=2y(y^(prime))^2+2 y^(y-4x y^(prime))=(y^(prime))^2

The solution of the differential equation y^(prime prime prime)-8y^(prime prime)=0, where y(0)=1/8,y^(prime)(0)=0,y^(prime prime)(0)=1 , is

If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c x and y(0)=0 , then

If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c x and y(0)=0 , then

If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c x and y(0)=0 , then

If a function is represented parametrically be the equations x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t , then which of the following statements are true? (a) y^('')(x-2x y^(prime))=y (b) y y^(prime)=2x(y^(prime))^2+1 (c) x y^(prime)=2y(y^(prime))^2+2 (d) y^('')(y-4x y^(prime))=(y^(prime))^2

If a function is represented parametrically be the equations x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t , then which of the following statements are true? (a) y^('')(x-2x y^(prime))=y (b) y y^(prime)=2x(y^(prime))^2+1 (c) x y^(prime)=2y(y^(prime))^2+2 (d) y^('')(y-4x y^(prime))=(y^(prime))^2