*EDIT: Whoops, wrong forum. This can be moved if needed. Sorry.
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.
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??
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...
Your separation of the variables is good up to here:
although I would write:
Now, in your next step, you pulled a out in front of the integral as if it were a factor, which is is not. You did not have:
If you did, then what you did would have been fine. So, let's go back to:
Let's multiply the integral on the left by
Now, observe that the integral on the left is of the form ...can you finish?