Problem with easy diffrential equation

[TheNaturalStep]

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

http://img209.imageshack.us/img209/7341/diffproblemsf9.jpg

Kindly TNS

 

[HallsofIvy]

You have
\frac{dm_p}{dt}= \dot{m_p_i}
In that case
m_p= \dot{m_p_i}t
would be correct only if \dot{m_p_i} was a constant.

 

[FrogPad]

First, check out https://www.physicsforums.com/showthread.php?t=8997

So you can type the math notation in \LaTeX.
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:
\frac{d m_p}{dt}= m_{pi}

Now your teacher says that m_p = m_{pi}t.

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

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

Original:
\frac{d m_p}{dt}= m_{pi}

You:
m_{pi} = m t^4

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

Now you say:
m_p = \frac{m_{pi} t}{5}

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