Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ranyai12

  • 2 years ago

Use Laplace transforms to find a nontrivial solution to tx''+(3t−4)x'+3x=0, x(0)=0 Require that x(1)=e^(−3) to find any arbitrary constant in your solution. x(t)=

  • This Question is Closed
  1. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Spacelimbus

  2. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I will have to work through this myself, but I am sure you have to use the fact that the LaPlace Transform is a linear operator, and then apply what this identity: \[\Large \mathcal{L} \lbrace x'(t) \rbrace =s Y(x(t))-x(0)\] which suits your initial conditions.

  3. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok but I thought you had to separate each part and do the laplace of that but im not a hundred percent sure because when I tried doing a different one I got it wrong

  4. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you mean separating t from x?

  5. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea but i think im wrong

  6. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I would try it the regular way to be honest and just chain the functions. Let me see.

  7. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    they are both in the same domain, time, so it would work from what I can tell.

  8. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  9. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\Large \mathcal{L}\lbrace t x''\rbrace = \frac{1}{s^2}( s^2Y(x(t))-sx(0)-x'(0)) \] *Repost*

  10. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok what do we do after that?

  11. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I am a bit lost here because of the initial conditions, we need them to be at t=0, so a change of variable could sole the problem we have with x'(0) maybe.

  12. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    otherwise I can't see how to find a solution, x(0)=0, but we require x'(0)

  13. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Otherwise it will be impossible to change from the s domain into the t domain.

  14. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    have you tackled a problem like this before? where they require you to change the setup?

  15. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no i havent which is why im so confused

  16. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is it maybe x'(1)=e^(-3) ?

  17. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no its x(0)=0 and x(1)=e^(-3)

  18. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    otherwise the only thing I can recommend you to do is carry out the steps normally to the end, maybe they want to keep it constant.

  19. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Did you see what I have done above? You just apply the LaPlace transform and then at the end you solve for Y(x(t))

  20. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but it tried doing that before and i ended up wrong

  21. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    just like the way I did above?

  22. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    For the first term \[\Large \mathcal{L}\lbrace t x''\rbrace = \frac{1}{s^2}( s^2Y(x(t))-\underbrace{sx(0)}_0-\underbrace{x'(0))}_c \]

  23. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    doing all of that to the three terms and then solving for big Y

  24. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but we dont have x'

  25. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you know the solution ?

  26. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no its an online hw assignment

  27. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    got any idea mate @Herp_Derp ?

  28. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I have the work for a different problem from my friend. would that help?

  29. Spacelimbus
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't know yet, but you can post it when you like, I haven't figured out yet how this problem could be tackled with the missing initial condition for the derivative. My assumption was that it could be derived at the end. But it doesn't seem to work out for me.

  30. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    here it is

    1 Attachment
  31. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh btw that whole ine is u(t-2)(t-)e^(-2)(e^(-2t))

  32. Herp_Derp
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Spacelimbus Your formula is wrong.\[\large \mathcal{L}\{ t\, x''(t)\}=-s^2\tilde{x}'(s)-2s\tilde{x}(s)+x(0)\]Further,\[\large \mathcal{L}\{(3t-4)x'(t)\}=3\mathcal{L}\{tx'(t)\}-4\mathcal{L}\{x'(t)\}=-3s\tilde{x}'(s)-(3+4s)\tilde{x}(s)+x(0)\]

  33. Herp_Derp
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Where\[\tilde{x}(s)=\mathcal{L}\{x(t)\}_{(s)}\]Is the transform of x.

  34. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok but this one ended up being correct. My friend solved for it and it ended up right but idk what she did exactly and she left back home for the rest of the summer and regarding to what you both said im totally lost im sorry

  35. Herp_Derp
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The end may be cut off on your browser:\[\ldots=-3s\tilde{x}'(s)-(3+4s)\tilde{x}(s)+4x(0)\]

  36. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    end of what

  37. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    nvr mind

  38. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok but do we o with that formula

  39. ranyai12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @myininaya @MathSofiya

  40. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.