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# Differential Equations watch

1. I am struggling a bit at the moment with differential equations, and wondering if anyone could help me with the following questions.

Given that y(o) = 50

y(t) + 0.5y(t-1) = 6

verify using t = 1 and t = 0 and analyze the stability of the system.

Describe in the nature of the time path and produce a graph of the latter

Thank you for your help i advance, and if you recommend any websites where i could further my knowledge it would be much appreciated
2. Are you able to write down y(1), y(2), etc?
3. (Original post by BabyMaths)
Are you able to write down y(1), y(2), etc?
i get y(t)=-23^t + 4 but i have a feeling thats really wrong
4. (Original post by BabyMaths)
Are you able to write down y(1), y(2), etc?
i get y= -19 and y(2) = 15.5
5. (Original post by ilikemaths1)
i get y= -19 and y(2) = 15.5
Keep going.

Do it on a calculator.

50=

6-ANS/2
=
=
=
....eventually...?
6. (Original post by BabyMaths)
Keep going.

Do it on a calculator.

50=

6-ANS/2
=
=
=
....eventually...?
eventually 4, what does that show?
7. You are asked to describe etc..

BTW, is part of the question missing?
8. (Original post by BabyMaths)
You are asked to describe etc..

BTW, is part of the question missing?
how do you verify the answer?

and the nature bit? :/

And onpe that seems to be all of it
9. Strange. If that's the whole question there doesn't seem to be anything to verify.

Your thread title suggests there should be a differential equation knocking around somewhere.

With just the behavior at t=0,1,2,3,4.. what can we say? It settles down to y=4 but what is y when t=101.1?

Sorry. I'm babbling.
10. (Original post by BabyMaths)
Strange. If that's the whole question there doesn't seem to be anything to verify.

Your thread title suggests there should be a differential equation knocking around somewhere.

With just the behavior at t=0,1,2,3,4.. what can we say? It settles down to y=4 but what is y when t=101.1?

Sorry. I'm babbling.
oh okay no problem, what you said was helpful anyways so thank you

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