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Math Help - differential equation for a sphere

  1. #1
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    differential equation for a sphere

    The rate of change of volume of a sphere is proportional to the volume of the sphere. Obtain a differential equation for the radius.


    I am keep getting kr/3 when the answer they gave in the textbook its from is 4kr please help for dr/dt
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  2. #2
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    Re: differential equation for a sphere

    Quote Originally Posted by righteous818 View Post
    The rate of change of volume of a sphere is proportional to the volume of the sphere. Obtain a differential equation for the radius.


    I am keep getting kr/3 when the answer they gave in the textbook its from is 4kr please help for dr/dt
    What you have written makes no sense. The question appears to be "Obtain a differential equation for the radius" but neither what you give as your answer, "kr/3", nor the answer you say is in the book "4kr", is a differential equation.

    Perhaps if you show what you have done to arrive at "kr/3" as a "differential equation" we could help.
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  3. #3
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    Re: differential equation for a sphere

    i meant that they want dr/dt, i got dr/dt= kr/3 while the book's answer is dr/dt= 4kr

    what i did is used chain rule

    dv/dt=dv/dr x dr/dt

    then dv/dt is proportional to v so
    dv/dt=k(4/3 x pi x r^3)

    then
    dr/dt= (dv/dt)/(dv/dr)
    = (k(4/3 x pi x r^3))/(4x pi x r^2)
    = kr/3

    but the answer they have is dr/dt= 4kr
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  4. #4
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    Re: differential equation for a sphere

    it could mean that the factor of 12 is incorporated into the constant k so that r'=4kr, where k2=k1/12
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