Home
Class 12
MATHS
Consider the family of all circles whose...

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`

Answer

Step by step text solution for 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 by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

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 y_(1) and y_(2) are the solution of the differential equation (dy)/(dx)+Py=Q, where P and Q are functions of x alone and y_(2)=y_(1)z, then prove that z=1+c.e^(-f(q)/(y_(1))dx), where c is an arbitrary constant.

Knowledge Check

  • If y=f(x),p=(dy)/(dx) and q=(d^(2)y)/(dx^(2)), then what is (d^(2)x)/(dy^(2)) equal to ?

    A
    `-(q)/(p^(2))`
    B
    `-(q)/(p^(3))`
    C
    `(1)/(q)`
    D
    `(q)/(p^(2))`

  • If y=f(x), p=dy/dx and q=(d^2y)/(dx^2) , then what is the value of (d^2x)/(dy^2) ?

    A
    `-q/p^2`
    B
    `-q/p^3`
    C
    `1/q`
    D
    `q/p^2`

  • The differential equation of the family of curves y = P(x+Q)^(2) is

    A
    `y y'' = (y')^(2)`
    B
    `2 y y'' = (y')^(2)`
    C
    2y y'' = y' + y
    D
    2y y'' = y' - y

    • Similar Questions

    Explore conceptually related problems

    A function y=f(x) satisfies the differential equation (d y)/(d x)+x^2 y=-2 x, f(1)=1 . The value of |f^(prime prime)(1)| is

    If x^(p)y^(q)=(x+y)^(p+q) , prove that (dy)/(dx)=(y)/(x)

    If p "and" q are the order and degree of the differential equation y(dy)/(dx)+x^3( d^2y)/(dx^2)+x y=cos x, then a. p q d. none of these

    If y=f(x)p=(dy)/(dx)" and q"=(d^(2)y)/(dx^(2)) . then what is (d^(2)x)/(dy^(2)) equal to ?

    If x^(p) + y^(q) = (x + y)^(p+q) , " then" (dy)/(dx) is

    Home
    Profile