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Form the differential equation represent...

Form the differential equation representing the family of curves `y = a sin ( x + b)`, where a, b are arbitrary constants.

Text Solution

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The correct Answer is:
`(d^(2)y)/(dx^(2)) + y = 0`
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Knowledge Check

  • If the order of a differential equation (d^2y)/(dx^2)-2 ((dy)/(dx))^3 +sin ((dy)/(dx)) +y =0 is l and the degree of the differential equation (1+(d^2y)/(dx^2))^(2/3)=[2-((dy)/(dx))^3]^(3/2) is m, then the differential equation corresponding to the family of curves y= Ax^l +Be ^(mx) , where A and B are arbitrary constants is

    A
    `(4x^2-2x)y^('') +(16x^2-2)y^'+(32x=8)y=0`
    B
    `(2x^2-x)y^('')+(8x^2-2)y^'+(16x-4)y=0`
    C
    `(2x^2-4t)y^('')-(8x^2-1)y^'+(16x-4)y=0`
    D
    `(4x^2-2x)y^('')+(8x^2-1)y^'+(16x-4)y=0`

  • Let p in IR , then the differential equation of the family of curves y = (alpha + beta x) e^(px) , where alpha, beta are arbitrary constants, is

    A
    `y'' = 4py' + p^(2)y = 0`
    B
    `y'' - 2py' + p^(2)y = 0`
    C
    `y'' + 2py' - p^(2)y = 0`
    D
    `y'' + 2py' + p^(2)y = 0`

  • Let p in IR , then the differential equation of the family of curves y = (alpha + beta x) e^(px) , where alpha, beta are arbitrary constant is

    A
    `y + 4py' + p^(2) = 0`
    B
    `y" - 2py' + p^(2) y = 0`
    C
    `Y" + 2 py' - p^(2) y = 0`
    D
    `y" + 2py' + p^(2) y = 0`

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    The differential equation representing the family of circles of constant radius r is

    The differential equation representing the family of circles of constant radius r is

    Let p in IR , then the differential equation of the family of curves y=(alpha +beta x)3e^(px) , where alpha,beta are arbitary constants , is

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