Differentials and Integrating

*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. (Headbang)

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...

Re: Differentials and Integrating

Quote:

Originally Posted by

**astuart** *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. (Headbang)

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...

First of all is a constant, so its integral will be . As for the LHS, rewrite it as so that you can use the substitution and the integral becomes .

Re: Differentials and Integrating

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?

Re: Differentials and Integrating

Quote:

Originally Posted by

**MarkFL2** 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?

I think so...However, I don't understand why became . I realize they're equivalent, but is there a reason for doing it?

Is this right? When I ran it through Wolfram, it gave me a different answer, which I just can't see how it got to that point..

Re: Differentials and Integrating

You forgot to include a parameter representing the constant of integration.