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The 2010, Honorary Member Welcoming, Undergraduate Degree Results Chat Thread Mk. IV watch

1. (Original post by Crazy Paving)
*****

Spoiler:
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8500
2. (Original post by Crazy Paving)
freetranslation.com innit?

Or just make your English words sound French.
I'm too English for all that tosh,

/excuse
3. (Original post by TheTallOne)
Consider the equation y" + ay' + by = 0 when b = (a^2)/4, so that the equation has a double solution m = -a/2. Suppose the differential equation has a solution of the form x(t) = u(t)e^mt. Prove that this is a solution if and only if u" = 0.

Well it is starting you in the face as you only need to show something

Ok, so you have y'' + ay' + (ya^2)/4=0
m^2+am+(ya^2)/4=0
Solve, get:
m=-a/2

Then you know that if you have a repeated root, your solution is of the form:
y=(A+Bt)e^mt

So therefore u(t)=(A+Bt) and u''=0

Now you need to then consider the case where u''=\=0 and then show that you can't have a solution.
(Hint: One way is 'Suppose u''=/=0' and show there's a contradiction or another way is to find y' and y'' and substitute in. Not sure if either works though as I cba to work through it. Remember u is a function of t so you need to use the product rule when finding y' and y'')
a solution to the equation is where x = 0 (or whatever the variable is).

and as e^mt can never equal 0, it's u(t) that has to equal 0, and that's only possible when u" = 0. I think Am I making sense?
4. (Original post by Loz17)
No-ones
I was just joking.

It does

Some old people who can;t swallow have the 6+ version though so you could have that one.
But I can swallow. No sexual stuff should be derived from that comment, thanks.

Well done.
5. are you guys quite posh then?
6. (Original post by Loz17)
Lets just run our own tests on it and see whats in there. some ir might help

7. (Original post by aliluvschoc)
I'm too English for all that tosh,

/excuse
I'm more English than you'll ever be.

(Original post by flowermaster91)
freshie
8. (Original post by + polarity -)

Ok then, Toby and I will do it ourselves like a proper chemistry geek couple
9. (Original post by Crazy Paving)
I'm more English than you'll ever be.

10. (Original post by Loz17)
Ok then, Toby and I will do it ourselves like a proper chemistry geek couple
11. (Original post by aliluvschoc)

orly?
12. (Original post by Loz17)
He wouldn't like that. He moans at me for talking to random people over the internet as it is

And you were too slow

Lets just run our own tests on it and see whats in there. some ir might help
I was just joking
And I know People think I'm weird for using TSR.
13. (Original post by Crazy Paving)
orly?

He wasn't a knight and didn't have a round table though.
14. (Original post by maxfire)
I was just joking
And I know People think I'm weird for using TSR.
He thinks I'm weird for being on here too. I've added a few people I've met from TSR into convos with him before. Never gone well

People just don't know the joys of TSR
15. (Original post by Loz17)
He thinks I'm weird for being on here too. I've added a few people I've met from TSR into convos with him before. Never gone well

People just don't know the joys of TSR
*****es don't know bout my TSR rep.

And I don't understand the GaGa law.
16. (Original post by aliluvschoc)

He wasn't a knight and didn't have a round table though.
My grandads were called Merlin and Arthur.

Spoiler:
Show
Not. Frank and Bert (we didn't know if it was Robert or Albert )
17. (Original post by Loz17)
Lol at this persons sig
I saw that earlier. However I had seen the gaga law prior to this after some of my friends joined the facebook group.
18. (Original post by + polarity -)
*****es don't know bout my TSR rep.

And I don't understand the GaGa law.
19. (Original post by sil3nt_cha0s)
a solution to the equation is where x = 0 (or whatever the variable is).

and as e^mt can never equal 0, it's u(t) that has to equal 0, and that's only possible when u" = 0. I think Am I making sense?
No. Remember u(t) is a function of t.

I've shown you the 'if' proof - just solve like normal and show that the general solution is of the form (A+Bt)E^mt (ie u(t)=A+Bt).

'only if' proof is more difficult, but I've given you two ideas which may work.

Perhaps you should have attended more lectures

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