# differential equation

• February 19th 2006, 05:45 AM
emterics90
differential equation
$m_{t+h}-m_{t}=hm_t$,

so $\frac{dm_t}{dt}=m_t$

I am told that you use differential equations to the get the differentiation above, but I don't see how. Can anybody see?
• February 19th 2006, 07:48 AM
CaptainBlack
Quote:

Originally Posted by emterics90
$m_{t+h}-m_{t}=hm_t$,

so $\frac{dm_t}{dt}=m_t$

I am told that you use differential equations to the get the differentiation above, but I don't see how. Can anybody see?

I will rewrite this as

$
m(t+h)-m(t)=hm(t)
$
,

so:

$\frac{dm}{dt}=m(t)$

So you are looking for a function which is its own derivative, so
something like:

$m(t)=Ae^t$

should do.

RonL