Can Someone Please Help! (problem is attached)

- anonymous

Can Someone Please Help! (problem is attached)

- jamiebookeater

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- anonymous

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- anonymous

@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!

- anonymous

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?

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## More answers

- anonymous

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

- anonymous

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

- anonymous

Can you check one answer?
\[\Large e^{-3t}+xe^{-3t}+e^{-t}-e^{-6t}+C \]
C not yet calculated.

- anonymous

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

- anonymous

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

- anonymous

A few adds here for the right hand side
\[\Large \mathcal{L}_t \lbrace \delta(t-1) \rbrace(s)=e^{-s} \]

- anonymous

whats C?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

no wait, C=1

- anonymous

ok let me check

- anonymous

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.

- anonymous

since we have initial conditions.

- anonymous

it's wrong:(

- anonymous

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

- anonymous

the other solution I got was this one
\[\Large 16te^{-3t}+e^{-t}-e^{-6t} \]

- anonymous

ok let me check

- anonymous

it's wrong :(

- anonymous

Did you come to this point @ranyai12 ?
\[\Large Y=\frac{e^{-t}-e^{-6t}+16}{(s+3)^2} \]

- anonymous

yea but dont we stop there

- anonymous

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

- anonymous

yea thats what I got earlier and it was wrong

- anonymous

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

- anonymous

oh

- anonymous

So inverse that and you should get the solution

- anonymous

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.

- anonymous

oh ok

- anonymous

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

- anonymous

I did the step and it ended up being wrong

- anonymous

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

- anonymous

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

- anonymous

yea that doesnt work

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

somewhere in my notes I have an error.

- anonymous

got that @ranyai12 ?

- anonymous

yea

- anonymous

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

- anonymous

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

- anonymous

yeh I will.

- anonymous

thank you!

- anonymous

no problem

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