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ranyai12

  • 2 years ago

Can Someone Please Help! (problem is attached)

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  1. ranyai12
    • 2 years ago
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  2. ranyai12
    • 2 years ago
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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!

  3. Spacelimbus
    • 2 years ago
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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?

  4. Spacelimbus
    • 2 years ago
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    General solution means, solving the homogenous differential equation, setting \(g(x)=0 \)

  5. Spacelimbus
    • 2 years ago
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    To find \(g(x)\) you can just take the inverse of the right hand side.

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

  7. Spacelimbus
    • 2 years ago
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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.

  8. Spacelimbus
    • 2 years ago
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    my guess is that only the first two are right, given by the homogenous system.

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

  10. ranyai12
    • 2 years ago
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    whats C?

  11. Spacelimbus
    • 2 years ago
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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.

  12. ranyai12
    • 2 years ago
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    you cant get partial credit so I can only check it at the end

  13. Spacelimbus
    • 2 years ago
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    hehe I actually get C=0 for the one above, so something looks dodgy

  14. Spacelimbus
    • 2 years ago
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    no wait, C=1

  15. ranyai12
    • 2 years ago
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    ok let me check

  16. Spacelimbus
    • 2 years ago
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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.

  17. Spacelimbus
    • 2 years ago
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    since we have initial conditions.

  18. ranyai12
    • 2 years ago
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    it's wrong:(

  19. Spacelimbus
    • 2 years ago
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    did you correct the x? Of course it should be there (-:

  20. Spacelimbus
    • 2 years ago
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    the other solution I got was this one \[\Large 16te^{-3t}+e^{-t}-e^{-6t} \]

  21. ranyai12
    • 2 years ago
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    ok let me check

  22. ranyai12
    • 2 years ago
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    it's wrong :(

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

  24. ranyai12
    • 2 years ago
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    yea but dont we stop there

  25. Spacelimbus
    • 2 years ago
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    \[\Large Y= \frac{e^{-s}}{(s+3)^2}- \frac{e^{-6s}}{(s+3)^2}+ \frac{16}{(s+3)^2} \]

  26. ranyai12
    • 2 years ago
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    yea thats what I got earlier and it was wrong

  27. Spacelimbus
    • 2 years ago
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    That's not the solution we've got to inverse it.

  28. ranyai12
    • 2 years ago
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    oh

  29. Spacelimbus
    • 2 years ago
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    So inverse that and you should get the solution

  30. Spacelimbus
    • 2 years ago
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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.

  31. ranyai12
    • 2 years ago
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    oh ok

  32. Spacelimbus
    • 2 years ago
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    try that and then please tell me if it's correct.

  33. ranyai12
    • 2 years ago
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    I did the step and it ended up being wrong

  34. ranyai12
    • 2 years ago
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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)

  35. ranyai12
    • 2 years ago
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    yea that doesnt work

  36. Spacelimbus
    • 2 years ago
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    I was checking on a similar problem and they attempt the problem the exact same way as we do.

  37. ranyai12
    • 2 years ago
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    i know thats what confused me! I did it twice and got the same asnwer

  38. Spacelimbus
    • 2 years ago
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    can your program read it? Or do you need to substitute something for the stepside function ??

  39. ranyai12
    • 2 years ago
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    i only have to substitute the theta to the wrod stepwhich i did and it was still wrong

  40. Spacelimbus
    • 2 years ago
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    somewhere in my notes I have an error.

  41. Spacelimbus
    • 2 years ago
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    got that @ranyai12 ?

  42. ranyai12
    • 2 years ago
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    yea

  43. Spacelimbus
    • 2 years ago
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    We are only two constants off but I can't see where I have made the algebraic error yet.

  44. ranyai12
    • 2 years ago
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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!

  45. Spacelimbus
    • 2 years ago
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    yeh I will.

  46. ranyai12
    • 2 years ago
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    thank you!

  47. Spacelimbus
    • 2 years ago
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    no problem

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