Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2012-07-20 06:01:30

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Differential equations

Post any interesting problems on differential equations here.

Here is one problem:

1)A man starts a business with 100,000$. Each year his profit is 20%, but he has to pay bills which sum up to 10,000$ annually. How much money do you predict he will have at the end of year 3 of his business?

Last edited by anonimnystefy (2012-07-21 01:00:38)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#2 2012-07-20 20:48:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Differential equations

Hi;

I get different answers depending on how I interpret the terms profit and bills. It sounds like bills are paid in a lump sum at the end of each year. Is profit continuous or is it also a lump sum at the end of the year?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#3 2012-07-21 00:40:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Differential equations

You can look at both as a sum at the end of the year.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#4 2012-07-21 00:59:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Differential equations


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#5 2012-07-21 01:01:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Differential equations

Whoops, I have just seen something in the problem. Changed 10% to 20%. Also, you may as well take profit to be made continuously over the year.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#6 2012-07-21 01:04:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Differential equations

Also, you may as well take profit to be made continuously over the year.

Now, you are talking.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#7 2012-07-21 01:06:26

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Differential equations

Yes.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#8 2013-01-27 00:12:05

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Differential equations

Have you got the answer?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#9 2013-01-27 01:01:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Differential equations

Hi;

I do not remember what it was.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#10 2013-01-27 01:16:47

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Differential equations

Well, there is a nice chance to do it again, if you want.

Last edited by anonimnystefy (2013-01-27 01:17:11)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#11 2013-01-27 01:22:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Differential equations

I am playing with it right now as you know. I am getting $141105.94 to the nearest penny. What do you get?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#12 2013-01-27 01:45:38

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Differential equations

I am getting $178101.29.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#13 2013-01-27 01:48:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Differential equations

Hmmmm, doesn't that seem high?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#14 2013-01-27 01:52:38

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Differential equations

Ih, sorry. Entered 1000 instead of 10000. Your answer is correct.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#15 2013-01-27 02:09:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Differential equations

Then I am getting

as the exact answer.

By the way have you seen my two latest math posts?

http://www.mathisfunforum.com/viewtopic.php?id=18885

http://www.mathisfunforum.com/viewtopic.php?id=18866


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#16 2013-01-27 03:29:29

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Differential equations

Yes, I have.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#17 2013-01-27 03:30:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Differential equations

What did you think?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#18 2013-01-27 05:19:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Differential equations

I alredy know the method for matrix decomposition you've shown in the first one.

I didn't have much time to work on the problems in the dice pdf, but I definitely will, when I have more time...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#19 2013-01-27 10:23:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Differential equations

Hmmm, so you already knew that one? How about matrix moves? You could not know that one.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#20 2013-01-27 11:32:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Differential equations

Which one is that?

Last edited by anonimnystefy (2013-01-27 11:33:29)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#21 2013-01-27 11:44:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Differential equations


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#22 2013-01-27 11:50:17

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Differential equations

I knew those as well...


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#23 2013-01-27 11:53:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Differential equations

Impossible, I invented that method. Gotcha!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#24 2013-01-27 13:20:39

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Differential equations

Nope. That is not correct.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#25 2013-01-27 14:16:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,302

Re: Differential equations

Yep, I invented the method of getting one element.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

Board footer

Powered by FluxBB