anonymous
  • anonymous
Can Someone Please Help! (problem is attached)
MIT 18.03SC Differential Equations
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
1 Attachment
anonymous
  • 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
  • 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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anonymous
  • anonymous
General solution means, solving the homogenous differential equation, setting \(g(x)=0 \)
anonymous
  • anonymous
To find \(g(x)\) you can just take the inverse of the right hand side.
anonymous
  • anonymous
Can you check one answer? \[\Large e^{-3t}+xe^{-3t}+e^{-t}-e^{-6t}+C \] C not yet calculated.
anonymous
  • anonymous
if none of that is correct, then I wouldn't know how to get this problem right, because of the delta function.
anonymous
  • anonymous
my guess is that only the first two are right, given by the homogenous system.
anonymous
  • anonymous
A few adds here for the right hand side \[\Large \mathcal{L}_t \lbrace \delta(t-1) \rbrace(s)=e^{-s} \]
anonymous
  • anonymous
whats C?
anonymous
  • 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
  • anonymous
you cant get partial credit so I can only check it at the end
anonymous
  • anonymous
hehe I actually get C=0 for the one above, so something looks dodgy
anonymous
  • anonymous
no wait, C=1
anonymous
  • anonymous
ok let me check
anonymous
  • 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
  • anonymous
since we have initial conditions.
anonymous
  • anonymous
it's wrong:(
anonymous
  • anonymous
did you correct the x? Of course it should be there (-:
anonymous
  • anonymous
the other solution I got was this one \[\Large 16te^{-3t}+e^{-t}-e^{-6t} \]
anonymous
  • anonymous
ok let me check
anonymous
  • anonymous
it's wrong :(
anonymous
  • anonymous
Did you come to this point @ranyai12 ? \[\Large Y=\frac{e^{-t}-e^{-6t}+16}{(s+3)^2} \]
anonymous
  • anonymous
yea but dont we stop there
anonymous
  • anonymous
\[\Large Y= \frac{e^{-s}}{(s+3)^2}- \frac{e^{-6s}}{(s+3)^2}+ \frac{16}{(s+3)^2} \]
anonymous
  • anonymous
yea thats what I got earlier and it was wrong
anonymous
  • anonymous
That's not the solution we've got to inverse it.
anonymous
  • anonymous
oh
anonymous
  • anonymous
So inverse that and you should get the solution
anonymous
  • 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
  • anonymous
oh ok
anonymous
  • anonymous
try that and then please tell me if it's correct.
anonymous
  • anonymous
I did the step and it ended up being wrong
anonymous
  • anonymous
i ended up getting (e^(-3t))(-e^(18)(t-6)step(t-6)+e^(3)(t-1)step(t-1)+16t)
anonymous
  • 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
  • anonymous
yea that doesnt work
anonymous
  • anonymous
I was checking on a similar problem and they attempt the problem the exact same way as we do.
anonymous
  • anonymous
i know thats what confused me! I did it twice and got the same asnwer
anonymous
  • anonymous
can your program read it? Or do you need to substitute something for the stepside function ??
anonymous
  • anonymous
i only have to substitute the theta to the wrod stepwhich i did and it was still wrong
anonymous
  • 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
  • anonymous
somewhere in my notes I have an error.
anonymous
  • anonymous
got that @ranyai12 ?
anonymous
  • anonymous
yea
anonymous
  • anonymous
We are only two constants off but I can't see where I have made the algebraic error yet.
anonymous
  • 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
  • anonymous
yeh I will.
anonymous
  • anonymous
thank you!
anonymous
  • anonymous
no problem

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