solving a differential equation.

**Yehia** · May 13th 2010, 07:41 AM

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

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

**Krizalid** · May 13th 2010, 08:46 AM

it's separable.

**Yehia** · May 13th 2010, 11:54 AM

Originally Posted by Krizalid

it's separable.

no its not!!! you cant really separate them...

**Krizalid** · May 13th 2010, 01:28 PM

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

**Yehia** · May 13th 2010, 01:32 PM

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.

**skeeter** · May 13th 2010, 01:34 PM

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

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

integrate both sides ...

**Yehia** · May 13th 2010, 01:43 PM

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 ?????

**skeeter** · May 13th 2010, 01:52 PM

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.

Thread: solving a differential equation.