Problem with easy diffrential equation

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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HallsofIvy
Homework Helper
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.

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,

$$\frac{d m_p}{dt}= m_{pi}$$

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?
$$\frac{d m_p}{dt} = \frac{d \left( \frac{m_{pi} t}{5} \right)}{dt} = ?$$