Question

Can Someone Please Help! (problem is attached)

Answer 1

@Spacelimbus Please help! I know I asked you before but good news is I figured the other one out! so, if you can please help!

Answer 2

hmm I don't have much practice with these, but if I am not completely mistaken then you have to find a general solution first and then a special solution?

Answer 3

General solution means, solving the homogenous differential equation, setting \(g(x)=0 \)

Answer 4

To find \(g(x)\) you can just take the inverse of the right hand side.

Answer 5

Can you check one answer?

\[\Large e^{-3t}+xe^{-3t}+e^{-t}-e^{-6t}+C \]
C not yet calculated.

Answer 6

if none of that is correct, then I wouldn't know how to get this problem right, because of the delta function.

Answer 7

my guess is that only the first two are right, given by the homogenous system.

Answer 8

A few adds here for the right hand side

\[\Large \mathcal{L}_t \lbrace \delta(t-1) \rbrace(s)=e^{-s} \]

Answer 9

whats C?

Answer 10

a constant, haven't solved, but I am at doubt that the solution is correct for the third and the fourth term in general.

Answer 11

you cant get partial credit so I can only check it at the end

Answer 12

hehe I actually get C=0 for the one above, so something looks dodgy

Answer 13

no wait, C=1

Answer 14

ok let me check

Answer 15

If that doesn't work, I believe we have to do it step by step and can't separate it, which will be more work but should work.

Answer 16

since we have initial conditions.

Answer 17

it's wrong:(

Answer 18

did you correct the x? Of course it should be there (-:

Answer 19

the other solution I got was this one

\[\Large 16te^{-3t}+e^{-t}-e^{-6t} \]

Answer 20

ok let me check

Answer 21

it's wrong :(

Answer 22

Did you come to this point @ranyai12 ?

\[\Large Y=\frac{e^{-t}-e^{-6t}+16}{(s+3)^2} \]

Answer 23

yea but dont we stop there

Answer 24

\[\Large Y= \frac{e^{-s}}{(s+3)^2}- \frac{e^{-6s}}{(s+3)^2}+ \frac{16}{(s+3)^2} \]

Answer 25

yea thats what I got earlier and it was wrong

Answer 26

That's not the solution we've got to inverse it.

Answer 27

oh

Answer 28

So inverse that and you should get the solution

Answer 29

It's a step side function, from what I think, which would make sense too, I made a mistake earlier by keeping the time domain.

Answer 30

oh ok

Answer 31

try that and then please tell me if it's correct.

Answer 32

I did the step and it ended up being wrong

Answer 33

i ended up getting (e^(-3t))(-e^(18)(t-6)step(t-6)+e^(3)(t-1)step(t-1)+16t)

Answer 34

http://www.wolframalpha.com/input/?i=laplace+transform+%28e%5E-s%29%2F%28s%2B3%29%5E2%29-+%28e%5E%28-6s%29%29%2F%28s%2B3%29%5E2%2B%2816%29%2F%28s%2B3%29%5E2

Answer 35

yea that doesnt work

Answer 36

I was checking on a similar problem and they attempt the problem the exact same way as we do.

Answer 37

i know thats what confused me! I did it twice and got the same asnwer

Answer 38

can your program read it? Or do you need to substitute something for the stepside function ??

Answer 39

i only have to substitute the theta to the wrod stepwhich i did and it was still wrong

Answer 40

http://www.wolframalpha.com/input/?i=x%27%27%2B6x%27%2B9x%3Ddelta%28t-1%29-delta%28t-6%29%2Cwith+x%280%29%3D2+and+x%27%280%29%3D2

Answer 41

somewhere in my notes I have an error.

Answer 42

got that @ranyai12 ?

Answer 43

yea

Answer 44

We are only two constants off but I can't see where I have made the algebraic error yet.

Answer 45

I ran out of tries anyway but thanks though and if you figure it out please let me knoe because it's killing me!

Answer 46

yeh I will.

Answer 47

thank you!

Answer 48

no problem