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