My Math Forum Homogeneous Second?Order Difference Equations

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October 6th, 2008, 06:24 AM   #1
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Homogeneous Second?Order Difference Equations

Alright...it is me again...and more to come... sorry... I am really bad in math..

Can someone help me understand everything after the general solution?

Why is 2A + 2B and -7A + 2B? Is there a formula to follow?

is (1) always minus (2)?

Where does the 9A comes from? Basically everything after General Solution. Thanks...
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October 6th, 2008, 10:15 AM   #2
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Re: Homogeneous Second?Order Difference Equations

Quote:
 Why is 2A + 2B and -7A + 2B? Is there a formula to follow?
Can you not see that there have been set up two equations which are then solved for values of A and B ...which can then be put into the general solution? In fact, it has been done for you. Being "really bad at math", do you really have to take this course of study? Life is too short to waste on things we don't want to do or can not do.

 October 6th, 2008, 05:10 PM #3 Newbie   Joined: Sep 2008 Posts: 11 Thanks: 0 Re: Homogeneous Second?Order Difference Equations Yes, Dave, I need to take this course, to understand this and to pass this..I am bad in this, that is why I need to learn.Sometimes in life we just can't choose what we want or do not want..
 October 6th, 2008, 06:22 PM #4 Senior Member   Joined: Jul 2008 Posts: 895 Thanks: 0 Re: Homogeneous Second?Order Difference Equations You have [had] found the general solution... $y_n= A( - 7)^n + B\left( 2 \right)^n$ You are told that ... $y_0= 2$ This means that n = 2, so sub that into the general solution: $2= A( - 7)^0 + B\left( 2 \right)^0$ What you seem not to know is that an exponent of 0 implies a value of 1. That is... 2 = A*1 + 2B*1 or A + 2B = 2 Similarly with... $y_1= 31$ substitute 1 for n: $31= A( - 7)^1 + B\left( 2 \right)^1$ That is 31 = -7A + 2B What you now have is a system of two equations in A and B, and can solve for them. My point is that all of this, including solving the two eqations is studied where I live in grade 9. Your studies should have had you master this and then much more before you started your present study which is a lead-in for studies in differential equations. My remarks were based upon the indicated lack of this firm background would mean that you will have to continually reach back into those studies and that can be overpowering in advanced studies that require this understanding already. I'm not saying to give up, and in fact wish you well. I am saying to get back to those pre-courses and take a fresh look at what you might be missing. That will require a good deal of effort. You need to be able to dog-paddle REALLY well if going into the deeper water. All I can add is "Good luck", and mean it sincerely.
 October 6th, 2008, 06:23 PM #5 Senior Member   Joined: Jul 2008 Posts: 895 Thanks: 0 Re: Homogeneous Second?Order Difference Equations You have [had] found the general solution... $y_n= A( - 7)^n + B\left( 2 \right)^n$ You are told that ... $y_0= 2$ This means that n = 0, so sub that into the general solution: $2= A( - 7)^0 + B\left( 2 \right)^0$ What you seem not to know is that an exponent of 0 implies a value of 1. That is... 2 = A*1 + 2B*1 or A + 2B = 2 Similarly with... $y_1= 31$ substitute 1 for n: $31= A( - 7)^1 + B\left( 2 \right)^1$ That is 31 = -7A + 2B What you now have is a system of two equations in A and B, and can solve for them. My point is that all of this, including solving the two equations is studied where I live in grade 9. Your studies should have had you master this and then much more before you started your present study which is a lead-in for studies in differential equations. My remarks were based upon the indicated lack of this firm background would mean that you will have to continually reach back into those studies and that can be overpowering in advanced studies that require this understanding already. I'm not saying to give up, and in fact wish you well. I am saying to get back to those pre-courses and take a fresh look at what you might be missing. That will require a good deal of effort. You need to be able to dog-paddle REALLY well if going into the deeper water. All I can add is "Good luck", and mean it sincerely.
 October 6th, 2008, 08:17 PM #6 Newbie   Joined: Sep 2008 Posts: 11 Thanks: 0 Re: Homogeneous Second?Order Difference Equations Hi Dave, Thanks...I really appreciate it. Anyway, I am currently doing my degree in InfoComm Technology and am quite surprise that I have to clear this Further Discrete Maths course.
October 7th, 2008, 04:19 AM   #7
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Re: Homogeneous Second?Order Difference Equations

Quote:
 Originally Posted by scarymovie Hi Dave, Thanks...I really appreciate it. Anyway, I am currently doing my degree in InfoComm Technology and am quite surprise that I have to clear this Further Discrete Maths course.
You are not alone. I don't do history. I can't do history. My memory simply fails me. My wife is a historian who can't do math and doesn't need to. We never argue; she remembers everything. Taking courses in math and physics, I despaired when I was told I had to take a compulsory course in political science [but not so much as did my history teacher in high school.] I squeeked through after a ton of hard work and visits to the prof for clarity. Someone once said that when an expert in some subject is taken out of that subject, he can be incredibly stupid. Well, I admit to that [not pretending to be expert in anything], but it didn't stop me from graduating, and it shouldn't stop you from becoming expert in what you will do best.

So .... DO take a fresh look a some past material [elementary algebra geometry trig] and try to get through it better than you did before. It's always worth the effort to skip a few nights in the pub.

October 8th, 2008, 06:37 PM   #8
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Re: Homogeneous Second?Order Difference Equations

Quote:
Originally Posted by Dave
Quote:
 Originally Posted by scarymovie Hi Dave, Thanks...I really appreciate it. Anyway, I am currently doing my degree in InfoComm Technology and am quite surprise that I have to clear this Further Discrete Maths course.
You are not alone. I don't do history. I can't do history. My memory simply fails me. My wife is a historian who can't do math and doesn't need to. We never argue; she remembers everything. Taking courses in math and physics, I despaired when I was told I had to take a compulsory course in political science [but not so much as did my history teacher in high school.] I squeeked through after a ton of hard work and visits to the prof for clarity. Someone once said that when an expert in some subject is taken out of that subject, he can be incredibly stupid. Well, I admit to that [not pretending to be expert in anything], but it didn't stop me from graduating, and it shouldn't stop you from becoming expert in what you will do best.

So .... DO take a fresh look a some past material [elementary algebra geometry trig] and try to get through it better than you did before. It's always worth the effort to skip a few nights in the pub.
THanks Dave for the piece of advise...gotta buck up now...

October 12th, 2008, 10:00 PM   #9
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Re: Homogeneous Second?Order Difference Equations

Hey..one more thing...I came across this while trying to solve the equation. May I know how am I suppose to get 2pine/3?
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 October 14th, 2008, 01:39 AM #10 Global Moderator   Joined: Dec 2006 Posts: 20,927 Thanks: 2205 That's the external angle of an equilateral triangle, so consider the geometry of such a triangle.

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