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
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}}}}
$
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
$