# solving a differential equation.

• May 13th 2010, 07:41 AM
Yehia
solving a differential equation.
hi, how yould you go about solving an equation like this?

$\displaystyle dv/dt=12.2 - kv$ ?? help very appreciated thanks!
• May 13th 2010, 08:46 AM
Krizalid
it's separable.
• May 13th 2010, 11:54 AM
Yehia
Quote:

Originally Posted by Krizalid
it's separable.

no its not!!! you cant really separate them...
• May 13th 2010, 01:28 PM
Krizalid
it is as long as "k" doesn't depend of "t."
• May 13th 2010, 01:32 PM
Yehia
Quote:

Originally Posted by Krizalid
it is as long as "k" doesn't depend of "t."

sorry, but i really dont understand what your saying. can you please just show me a step further and help me out because i really am lost :( i would really appreciate it.
• May 13th 2010, 01:34 PM
skeeter
$\displaystyle \frac{dv}{12.2 - kv} = dt$

$\displaystyle \frac{-k}{12.2 - kv} \, dv = -k \, dt$

integrate both sides ...
• May 13th 2010, 01:43 PM
Yehia
Quote:

Originally Posted by skeeter
$\displaystyle \frac{dv}{12.2 - kv} = dt$

$\displaystyle \frac{-k}{12.2 - kv} = -k \, dt$

integrate both sides ...

how come you just removed dv from the equation?

and so whats the general solution? is it : v= (ae^-kt - 12.2)/-k ?????
• May 13th 2010, 01:52 PM
skeeter
Quote:

Originally Posted by Yehia
how come you just removed dv from the equation?

and so whats the general solution? is it : v= (ae^-kt - 12.2)/-k ?????

didn't mean to "remove it" ... just a typo. it's fixed.