Problem with easy diffrential equation

  • #1
Problem with an easy diffrential equation, the problem is explained in the picture ....

http://img209.imageshack.us/img209/7341/diffproblemsf9.jpg [Broken]

Kindly TNS
 
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Answers and Replies

  • #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.
 
  • #3
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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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