*EDIT: Whoops, wrong forum. This can be moved if needed. Sorry.

Hello,

I'm really having a bit of trouble here. I'm doing an online course with limited recorded lectures and a textbook which is helpful only some of the time, so I'm hoping for a little bit of guidance here.

I have problem in which I've managed to write a differential equation to represent the problem. In the problem, C is defined as calories per day, so it's not an 'arbitrary constant'. I'm supposed to solve the equation, but I don't really know how to go about it.

$\displaystyle \frac {dw}{dt} = \frac {C-17.5w}{3500}$

$\displaystyle = \frac {1}{C-17.5w} \, \frac {dw}{dt} = \frac {1}{3500} $

$\displaystyle = \int \frac {1}{C-17.5w}\,dw = \int 3500^{-1} dt$

I fall down a little bit here, as I don't know exactly how to deal with C (the constant), whether the dt on the right, is just t??

$\displaystyle = \frac{1}{C} \, \int \frac {1}{-17.5w} dw = \frac {1}{3500t} + M$

$\displaystyle = \frac {1}{C} \, -17.5\,ln|w| = \frac {1}{3500t} + M$

From here it just kind of falls to pieces, and I don't know whether I am supposed to get the 1/C to the other side, then divide by 17.5, then get rid of the natural log, or whether I messed up an earlier step.

I really wish the lectures explained this sort of question a little better...