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# Need Help On Differential Equations

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Need Help On Differential Equations

alright so i have a problem with integrating the differential equation

dM/dt = 100 - kM

i have to separate the variables and then integrate the diffrerential equation to get an equation for M in terms of t. For the initial condition, M=0 when t=0

just for reference
my book is

CALCULUS
concepts and applications
2nd ed
key curriculum press

and the problem is in page 329 CH7 sec 3 Problem #1 c

any help will be greatly appreciated, thnx

:D Cal Golden Bears, HERE I COME!!!:D

:D Go Bears!!!!:D

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Joined: Mar 2005

multiply by dt, divide by (100 - kM), integrate, solve for M

The tricky part is seeing that it's all that under dM

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thnx
i got far with ur explanation
thou i still havent come up with right the answer

:D Cal Golden Bears, HERE I COME!!!:D

:D Go Bears!!!!:D

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Joined: Oct 2005

OKay, well, I tried this problem and I assumed k was a constant...(if I am wrong let me know) But thento integrate I used u substitution and it was very easy...so maybe try that.

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I'm getting:

(100 - e^t)/k = M

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"I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."
"But," say Man, "the Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It

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I got something similar when I redid it and it was M= k^2e^t+100 + C

Then when you plug in the initial condition...i got lost.

There is no future. There is no past. There's only us, there's only this. Forget regret or life is your to miss. No other road, no other way. No Day But Today!!!

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Okay, I forgot about the C...Yeah, I'm out of practice. Too many matricies in my brain I suppose. But I redid it and I'm not exactly sure what you did stupidgurl2boiz...

With the C I got M = (100 - Ce^t)/k

And with the initial condition I found that C = 100, so it's:

M = 100(1 - e^t)/k

And that's what I got...

[=RoyalBlue][=Comic Sans MS]
"I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."
"But," say Man, "the Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It

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Joined: Oct 2005

OKay I totally got it! I asked a calc teacher and she got M=100/k(1-e^-kt)

which now that I look, it is the same thing pianogirl got....lol you got to it before i did!

There is no future. There is no past. There's only us, there's only this. Forget regret or life is your to miss. No other road, no other way. No Day But Today!!!

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pianogirl2422 wrote:Okay, I forgot about the C...Yeah, I'm out of practice. Too many matricies in my brain I suppose. But I redid it and I'm not exactly sure what you did stupidgurl2boiz...

With the C I got M = (100 - Ce^t)/k

And with the initial condition I found that C = 100, so it's:

M = 100(1 - e^t)/k

And that's what I got...

mmm....
so close:)

actually, after your first tip i was able to get quite far with my procedure
and i arrived at the same answer as you have
but:eek:
there is some weird step necessary
it goes as follows

dM/dt = 100-kM
dM/(100-kM) = dt

then we integrate and use that weird step (in red)

-1/k S dM/(100-kM) = S dt
-1/k ln |100-kM| = t+C
ln 100-kM = -kt-kC
100-kM = e^-kt-kC
-kM = Ce^-kt -100
M = (Ce^-kt -100)/-k

substitute the initial conditions
0 = 1/k (100 - C^-k0)
100 = C

thus,

M =100/k (1-e^-kt)
:D

the same as the answer stupidgurl2boiz got from asking the calc teacher

it sure did take a while to get to this answer and i had to carefully review some notes that I was lucky to have from the section in which the problem was

oh, btw, the answer i got is the same as the one in the teacher's manual but i still don't know why there is a need to factor the -1/k when we integrate:confused:

any ideas??

thnx for the help

:D Cal Golden Bears, HERE I COME!!!:D

:D Go Bears!!!!:D

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Joined: Oct 2005

Because k respesents a constant...when you integrate you use u-substitution right? well, your u was 100-km which meant your du would be -kmdm . SInce the integral only contains mdm you have to factor out the -k. Thus you would have -1/kdu=m dm and then you can procede with u-substitution.

There is no future. There is no past. There's only us, there's only this. Forget regret or life is your to miss. No other road, no other way. No Day But Today!!!

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Stupid chain rule...I really am out of practice...

[=RoyalBlue][=Comic Sans MS]
"I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."
"But," say Man, "the Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It

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