hi all,

Im having trouble solving this differential equation, ive tried many times but just cant seem to get my algebra correct >.< and hence end up getting stuck.

$\displaystyle

dv/dt = -g - bv/m

$

pls help me

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- Apr 27th 2008, 08:39 AMtasuketedifferential equation help >.<
hi all,

Im having trouble solving this differential equation, ive tried many times but just cant seem to get my algebra correct >.< and hence end up getting stuck.

$\displaystyle

dv/dt = -g - bv/m

$

pls help me - Apr 27th 2008, 08:40 AMMathstud28
- Apr 27th 2008, 08:44 AMtasukete
- Apr 27th 2008, 08:45 AMtasukete
this is actually a physics question where b is the drag coefficient, g is gravity, m is mass, v is velocity

- Apr 27th 2008, 08:46 AMtasukete
im asked to find the velocity, v, in terms of t,b,g,m

- Apr 27th 2008, 08:47 AMMathstud28
- Apr 27th 2008, 08:48 AMPaulRS

We have: $\displaystyle

\frac{{v'}}

{{g + \tfrac{{b \cdot v}}

{m}}} = - 1 \Rightarrow \int_0^t {\frac{{v'}}

{{g + \tfrac{{b \cdot v}}

{m}}}dt} = - t

$

Now let $\displaystyle u=v$ on the left hand side and it follows easily

$\displaystyle

\int_0^t {\frac{{v'}}

{{g + \tfrac{{b \cdot v}}

{m}}}dt} = \int_{v\left( 0 \right)}^{v\left( t \right)} {\frac{{dv}}

{{g + \tfrac{{b \cdot v}}

{m}}}}

$

;) - Apr 27th 2008, 08:51 AMtasukete
- Apr 27th 2008, 08:53 AMPaulRS
- Apr 27th 2008, 09:08 AMtasukete
- Apr 27th 2008, 09:29 AMtasukete
can i ask for a confirmation. unsure whether this is correct direction to take..

$\displaystyle

\frac{dv}{dt} = -g - \frac{bv}{m}

$

$\displaystyle

\frac{dt}{dv} = \frac{-1}{g} - \frac{m}{bv}

$

$\displaystyle

t = \int \frac{-1}{g} - \frac{m}{bv}dv

$

$\displaystyle

t = \frac{-v}{g} - \frac{m}{b}logv + c

$ - Apr 27th 2008, 09:34 AMMoo
- Apr 27th 2008, 09:39 AMtasukete
- Apr 27th 2008, 09:57 AMtasukete
$\displaystyle

\frac{dv}{dt} = -g - \frac{bv}{m}

$

$\displaystyle

\frac{dv}{dt} = \frac{-gm - bv}{m}

$

$\displaystyle

\frac{dt}{dv} = \frac{m}{-gm - bv}

$

$\displaystyle

t = \int \frac{m}{-gm - bv}dv

$

$\displaystyle

t = -m log(gm + bv) + c

$