Question

Find the solution of the IVP

Answer 1

E. all of the above

Answer 2

\[y''+5y'+6y=u(t-1)+\delta(t-2)\\y(0) = 0;\text{ }y'(0)=1\]

@amistre64 @zepdrix
Please help!
I have no idea where to start and in what direction to head with this stuff

Answer 3

You have to use laplace transforms.

Answer 4

Remember those?

Answer 5

Yip, I know. That is the whole point of the problem

Answer 6

Do you know how to take the laplace transform of a second order differential equation, as well as a heaviside and dirac function?

Answer 7

I am busy studying Laplace/Heaviside/Dirac delta for tomorrow's exam, but don't have a clue how Heaviside and Dirac work. I only have one example of each and I don't understand how they work and what to do :(

Answer 8

The only difference between heaviside/dirac and regular laplace transform is that they deal with an offset in time
For example: instead of e^9t, you'd have e^9(t-3)

Answer 9

If I understand this problem correctly, it consists of a Heavisede part and a Dirac part, right?

Could you please help me with this step by step, if you dont mind?

Answer 10

First off, lets convert this equation in terms of S by taking the laplace transform of every term in the equation. Can you do that?

Answer 11

Was there a subscript next to your U on your heaviside function? That's important

Answer 12

I got \[s^2Y-1+5sY+6Y = ???\]
but don't know what goes in the place of the ???

I've never had any subscripts at that u, so I don't know what that means. This question didn't have one

Answer 13

I'll have to do a bit of research. The subscript on U tells us how much time is offset!

Answer 14

Wow! I thought my book wasn't very well written out..

Answer 15

Yeah I have no idea what to do. I really don't like our textbook, so little is explained...

Answer 16

There is supposed to be a subscript on u telling us how much time is shifted, otherwise there just isn't enough information.

Answer 17

I don't know...

Answer 18

@zepdrix can you help?

Answer 19

LOL if Zepdrix sees another Differential Equation problem..

Answer 20

I thought you left, it doesn't show your name..

Answer 21

Hmm crap I can't remember how to deal with the unit step and delta function :( Hmm

Answer 22

I almost got the correct answer this time. My textbook only shows answers to the problems

Answer 23

I cracked this pellet, by the way hahaahah

Answer 24

what! it autocorrected pellet haha

Answer 25

oh cool c :

Answer 26

IDK what subscript you're talking about; \(u(t-1)\) will be \(0\) for \(t<1\) and \(1\) for \(t\ge1\) -- it's just shifting our standard unit step function to the right one.