# Dp/dt = 4p-3p^2-p^3Diff. Equation.

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## Answers and Replies

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I see a mistake in the second line which probably creates problems further down... 4-3p-p^2 factors as (4+p)(1-p) not (4-p)(1+p)...gotta watch those negative signs, they'll getcha every time. :)

I see a mistake in the second line which probably creates problems further down... 4-3p-p^2 factors as (4+p)(1-p) not (4-p)(1+p)...gotta watch those negative signs, they'll getcha every time. :)
haha, thanks.... Though, it sucks I made the mistake so early......

I think theres an intigration mistake in line three...should be (1/4)ln(p) - (1/20)ln(4+p) - (1/5)ln(1-p)...I think. That should help with the simplification.

How do you interat it???

I broke it down, and use a U-sub on all of them.
Ex: INT 1/(80+20P) dp
U = 80 + 20P
du = 20 dp
1/20du = dp
1/20 INT 1/U du
1/20 ln | U | + C
Resub: 1/20 ln |80+20P| + C

Can you pull the 1/20 out in front?

You can always double check by differentiating your integration result to see if it is the same as what you started with. But yeah, remember you can pull a constant out front when integrating...if you had something like INT(1/6x) thats the same as (1/6)INT(1/x)

You can always double check by differentiating your integration result to see if it is the same as what you started with. But yeah, remember you can pull a constant out front when integrating...if you had something like INT(1/6x) thats the same as (1/6)INT(1/x)
How do you handled after this point though. The other I knew how to do, just made a few little errors.

I know, LN A - LN B = LN A/B

I also know, 1/A LN |B| = LN Aroot of B

Once I get them all to LN Some-Root B, I can get them all to the same LN. and will I take the e of both sides the LN is gone....

What do I do that at that point I have A-Root-# * B Root-# / C root - #

I don't know how to handle all the roots.

Do you know what the answer is supposed to be? I've been playing around with the math a bit and I get to (1/20) ln [(p^5) / (4+p)((1-p)^4)] After that I just kind of gave up because I'm lazy. :) I guess I just assumed that simplified algebraically...is it supposed to be a nice clean answer like p = f(t) ?

I don't know the answer, but it does need to be P (t) = F(t). Because after we are done, we need to use a few initial conditions.... P(0)= 3, P(0)= -1/2, P(0)= -2.

Hmm, I'm not sure and its my bed time. I'll give it a little thought and get back to you tomorrow. Hopefully someone else on the forum can give you some advice in the mean time.

sounds good. Thanks, you have been a lot of help :)

I tried anyway. Sorry I couldn't have been more helpful...I'm just so lazy. :D