# Thread: solving a differential equation.

1. ## solving a differential equation.

hi, how yould you go about solving an equation like this?

$dv/dt=12.2 - kv$ ?? help very appreciated thanks!

2. it's separable.

3. Originally Posted by Krizalid
it's separable.
no its not!!! you cant really separate them...

4. it is as long as "k" doesn't depend of "t."

5. 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.

6. $\frac{dv}{12.2 - kv} = dt$

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

integrate both sides ...

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

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

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 ?????

8. 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.