Year 12s: what will be the first way you research your future options? >>

Differential Equations

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

Reply 1

BabyMaths

Are you able to write down y(1), y(2), etc?

Reply 2

ilikemaths1

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

Reply 3

ilikemaths1

Original post by BabyMaths

Are you able to write down y(1), y(2), etc?

i get y= -19 and y(2) = 15.5

Reply 4

BabyMaths

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...?

Reply 5

ilikemaths1

Original post by BabyMaths

Keep going.

Do it on a calculator.

50=

6-ANS/2
=
=
=
....eventually...?

eventually 4, what does that show?

Reply 6

BabyMaths

You are asked to describe etc..

BTW, is part of the question missing?

Reply 7

ilikemaths1

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

Reply 8

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.

Reply 9

ilikemaths1

Original post by BabyMaths