Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

Differentiation Question

Last edited by Au101 (2011-08-04 06:39:17)

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Differentiation Question

Oh I think I've got it, let's see:

Last edited by Au101 (2011-08-04 07:04:41)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Differentiation Question

hi Au101

what is y?

---

“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
The knowledge of some things as a function of age is a delta function.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Differentiation Question

Well it was y that was confusing me, actually, to be honest - the context of the question is a linear second order ordinary differential equation.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Differentiation Question

hi Au101

i suggest we wait for other guys to come up with their solutions.also i think you should just express dx and dx^2 in terms of dz,d^2 z and dz^2.

---

“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
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Differentiation Question

hi Au101,

Post 2 is correct.

Then make your substitution and cancel a cos cubed factor to get to the required form.  Have you done this yet?

The final step looks similar to a simple harmonic motion DE.  (solutions of the form cos(wx))

I've got to go out now, so I'll have a proper look later on this morning (8.45 now)

edit at 10.45  :  Oh no it isn't.

the general solution to the complementary equation

is

edit: not quite.  read on

Now for a particular solution; which eludes me at the moment ??

new edit at 11.03:

Got it

particular solution is

I think that means the general solution of the original equation is:

(This is not my area so someone else chip in please .....  )

final edit at 13.47.

gAr has tidied this up to a more elegant answer without the root 2s alongside the constants in post #9.

Bob

Last edited by Bob (2011-08-05 00:50:42)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Differentiation Question

Hi Bob,

The solution which a CAS gives for

is

Was the question about solving a DE or forming a DE?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Differentiation Question

hi gAr

Yes, thanks.  That's what I meant to say of course.  Whoops!  What's a root 2 amongst friendly constants?

See post #4.  He wants it solved.

Bob

Last edited by Bob (2011-08-05 00:06:10)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Differentiation Question

Hi Bob,

Okay, Now I see it!

The solution for #4 is

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Differentiation Question

hi gAr

Thanks for looking at that.  Mine was almost there; in fact ok if you amalgamate the root 2s into the constants;  so a useful bit of revision for me.  I'll edit my ealier post (not to make it look as though I did it; but to direct Au101 to your solution.

Ta! 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Differentiation Question

Hi Bob,

Yes, the √2 in your solution doesn't matter. It's yet another constant!
I think I wasn't paying attention.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Differentiation Question

Hi guys, thanks a lot.

Yep, that's exactly what I got. Well, I gave y in terms of x, of course, but it's the same thing:

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Differentiation Question

Hi Au101,

You're welcome!
Thanks to Bob, who did most of the work here.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Differentiation Question

You're quite right, although I value your contribution as well. Nevertheless, I'm very grateful to you Bob, for going on and helping with the rest of the question, especially if this is not your area .

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Differentiation Question

We all enjoy learning. If it's not our area, we would enjoy staying there for some time.
Just like going for a hike!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Differentiation Question

I couldn't agree more

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Differentiation Question

hi Au101,

You're welcome.  If a post is in my area, then it's easy to post back but I don't learn anything.  If it's buried deep in my memory, then I enjoy re-visting the topic and reminding myself how it goes.  Those posts are more satisfying to attempt.

I felt a bit lacking in confidence with this one.  I was expecting at any moment you would come back with some searching question about what I'd done;  then I'd look a right fool as my weakness would be exposed. So ......

to gAr: many, many thanks for getting involved too;  it was a great boost to my confidence when I saw your solution.  Phew!  Long hike indeed!

All the best to you both,

 

Bob

Last edited by Bob (2011-08-05 03:38:24)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Differentiation Question

Hi Bob,

Thanks to computer for solving it! I only posted that answer.

I think it would be nice to have all the common methods for DE under "formulas", so we can quickly refer that.
I'll see if I can collect something.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Differentiation Question

hi gAr

As you may have worked out by now, I learnt my maths in a era before computers were widely used;  I did calculations long hand or by logs; and anything else on a piece of paper.  The second school I taught in was one of the first in the country to get a computer; wow! just the one;  it was an RM 380Z ( job adverts in the TES would describe it as a 38 oz computer.  as if any one could make a computer that weighed so little!)  using 5.25" floppy discs for it's operating system and then for programming languages.  Oh how lucky we thought we were. 

And then, in my next school we took part in a trial of the Post Office's Prestel system for communicating down the telephone line through an acoustic coupler and a plug in switch-board.

Oh how have things changed?

So I tend to do my questions long hand.  Beside me now, I have a lot of sheets of paper with all my scribblings.  But you mustn't think I'm nostalgic for the 'good old days'.  After all I am using a computer now. 

Bob

Last edited by Bob (2011-08-05 04:11:08)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Differentiation Question

Hi Bob,

Yes, I understand!

But I too studied doing problems by hand, since I wasn't aware of the programs, and the internet was too slow  and too expensive to download anything.
It's only since a past few months I'm using a computer for calculation, that too only if the problem appears tedious to do by hand, or I don't remember a result.
Otherwise, it's faster to think than to type!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Differentiation Question

Hi Bob,

I agree and personally, I prefer to work out a solution by hand where it's feasible - it's more satisfying. I can post my full solution for you if you're interested - see if our methods have changed