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The form of the differential equation of...

The form of the differential equation of the central conics `ax^(2) + by^(2) = 1` is

A

`x = y (dy)/(dx)`

B

`x((dy)/(dx))^(2) + xy (d^(2)y)/(dx^(2)) - y (dy)/(dx) = 0`

C

`x + y (d^(2)y)/(dx^(2)) =0`

D

None of the above

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • The form of the differential equation of the central conics, is

    A
    `x=y(dy)/(dx)`
    B
    `x+y(dy)/(dx)=0`
    C
    `x((dy)/(dx))^(2)+xy(d^(2)y)/(dx^(2))=y(dy)/(dx)`
    D
    none of these

  • What is the differential equation of the curve y= ax^(2) + bx ?

    A
    `x^(2) "" (d^(2) y)/(dx^(2)) - 2 x"" (dy)/(dx) + 2y =0`
    B
    `x^(2) "" (d^(2)y)/(dx^(2)) - y ((dy)/(dx))^(2) + 2 = 0`
    C
    `(1-x)^(2) (d^(2) y)/(dx^(2)) - (y ""(dy)/(dx))^(2) = 0`
    D
    None of these

  • If a and b are arbitrary constants, then the order and degree of the differential equation of the family of curves ax^(2)+by^(2)=2 respectively are

    A
    2, 2
    B
    1, 2
    C
    1, 1
    D
    2, 1

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