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The diff. equation of the family of stra...

The diff. equation of the family of straight lines y = mx is `(dy)/(dx)-x=0`.

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Knowledge Check

  • The differential equation of the family of straight line y=mx+(4)/(m) , where m is the parameter, is

    A
    `x(dy)/(dx)=0`
    B
    `(x-y)(dy)/(dx)=4`
    C
    `x((dy)/(dx))^(2)-y(dy)/(dx)=4`
    D
    `x((dy)/(dx))^(2)-y(dy)/(dx)+4=0`

  • The differential equation of the family of straight lines whose slope is equal to y-intercept, is

    A
    `(x+1)(dy)/(dx)-y=0`
    B
    `(x+1)(dy)/(dx)+y=0`
    C
    `(dy)/(dx)=(x-1)/(y-1)`
    D
    `(dy)/(dx)=(x+1)/(y+1)`

  • The differential equation of the family of straight lines whose slope is equal to y - intercept ,is

    A
    ` (x+1)(dy)/(dx)-y = 0`
    B
    ` (x+1)(dy)/(dx)+y = 0`
    C
    ` (dy)/(Dx)=(x+1)/(y-1)`
    D
    `(dy)/(Dx)=(x+1)/(y+1)`

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    Explore conceptually related problems

    Which one of the following differential equations represents the family of straight lines which are at unit distance from the origin a) (y-x(dy)/(dx))^2=1-((dy)/(dx))^2 b) (y+x(dy)/(dx))^2=1+((dy)/(dx))^2 c)(y-x(dy)/(dx))^2=1+((dy)/(dx))^2 d) (y+x(dy)/(dx))^2=1-((dy)/(dx))^2

    Statement 1: The differentia equation of the family of curves represented byy =Ae^(x) is given by (dy)/(dx)=y statement 2:(dy)/(dx)=y is valid for every member of the given family.

    [" The differential equation of the family of curves "],[y=c_(1)x^(3)+(c_(2))/(x)" where "c_(1)" and "c_(2)" are arbitrary "],[" constants,is "],[" O "x^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)+3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))-x(dy)/(dx)+3y=0]

    Show that the differential equation of the family of circles having their centres at the origin and radius 'a' is : x+y (dy)/(dx)=0 .

    Form of the differential equation of all family of lines y=mx+(4)/(m) by eliminating the arbitrary constant m is

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