Help needed please!

Ok so I really need help with this question for an assignment.

There are 2 MP3 players (A and B) and pretty much I need to decide which one is better ie. which has the longest playback time.

The percentage of battery life A(t) for the mp3 player A is given by:

(100-t^2)\frac{dA}{dt}+4tA = 0

with A(0)=100

The percentage of battery life B(t) for the mp3 player B is given by:

100\frac{dB}{dt}-B^2+10000 = 0

with B(0)=100tanh(12) which is just 100

First, I tried rearranging both equations to make

\frac{dA}{dt}

and

\frac{dB}{dt}

the subjects in both cases.

So I ended up with:

A = -\int \frac{4tA}{100-t^2}

B = \int \frac{B^2 + 10000}{100}

but then I don't know how to integrate that because of the A and the B in the equations.

A hint was also given: Do not use partial fractions to do the integration. Use the fact that:

\frac{d}{dx}(arctanhx) = \frac{1}{1-x^2}

Thanks in advance for those who can help!!!

Reply 1

Ewan

15

A is independent of t therefore it is a constant in this case. Although, why don't you just divide by t?

Spoiler

Do similar with the second.

Reply 2

coscos

OP

Ewan

A is independent of t therefore it is a constant in this case. Although, why don't you just divide by t?

I thought I might be able to separate 4A from the integral but wasn't sure if that was ok.

And I didn't think of just dividing by t, so that means I should just get:
1/(100 - t^2) in the integral if I take out 4a, yes?

Reply 3

generalebriety

16

coscos

I thought I might be able to separate 4A from the integral but wasn't sure if that was ok.

And I didn't think of just dividing by t, so that means I should just get:
1/(100 - t^2) in the integral if I take out 4a, yes?