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Problem with easy diffrential equation

  1. Sep 26, 2006 #1
  2. jcsd
  3. Sep 26, 2006 #2

    HallsofIvy

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    You have
    [tex]\frac{dm_p}{dt}= \dot{m_p_i}[/tex]
    In that case
    [tex]m_p= \dot{m_p_i}t[/tex]
    would be correct only if [itex]\dot{m_p_i}[/itex] was a constant.
     
  4. Sep 26, 2006 #3
    First, check out https://www.physicsforums.com/showthread.php?t=8997

    So you can type the math notation in [itex] \LaTeX [/itex].
    To see how I typed things in the "math" click on the images and you will see the code. It's very easy, and the preferable way to communicate.


    Second,

    So your equation is:
    [tex] \frac{d m_p}{dt}= m_{pi} [/tex]

    Now your teacher says that [itex] m_p = m_{pi}t [/itex].

    You are saying this:
    Let [itex] m_{pi} = m t^4 [/itex].
    Then,
    [tex] m_p = \frac{m_{pi} t}{5} [/tex]

    You are not consistent with your notation. You should be careful here. For example, you introduce the variable [itex] m [/itex] and then it just disappears. However, with your argument you have:

    Original:
    [tex] \frac{d m_p}{dt}= m_{pi} [/tex]

    You:
    [tex] m_{pi} = m t^4 [/tex]

    If we sub this in:
    [tex] \frac{d m_p}{dt} = (m t^4) [/tex]

    Now you say:
    [tex] m_p = \frac{m_{pi} t}{5} [/tex]

    What happens if you differentiate this?
    [tex] \frac{d m_p}{dt} = \frac{d \left( \frac{m_{pi} t}{5} \right)}{dt} = ? [/tex]
     
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