Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Nisha318 Group Title

Differential Equations-> Laplace-> Piecewise Defined functions. Solve the initial value problem.

  • 3 years ago
  • 3 years ago

  • This Question is Closed
  1. Nisha318 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    • 3 years ago
    1 Attachment
  2. abtrehearn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    L{y'+3y} = (s - 3)Y(s) - 1.\[L \left\{ f(x) \right\} = \int\limits_{0}^{\pi}e ^{-s x}\sin x dx\]\[= (e^{-\pi x} - 1)/(s^{2} + 1),\]so \[(s - 3)Y(s) - 1 = (e^{-\pi s} - 1)/(s^{2} + 1),\]giving us\[Y(s) = 1/(s + 3) + \[(e^{-\pi s} - 1)/[(s^{2} + 1)(s + 3)]\].\]No problem finding \[L^{-1}\left\{ 1/(s + 3 \right\}.\]To find\[L^{-1}\left\{ (e^{-\pi s} - 1)/[(s^{2} + 1)(s + 3) \right\}, \]we can use the convolution theorem. We know that\[L^{-1}\left\{ (e^{-\pi s} - 1)/(s^{2} + 1)\right\} = f(x),\]so the inverse laplace transform works out to \[f(x) * e^{-3x} = \int\limits_{0}^{x}f(u) e^{-3(x - u)}du.\]

    • 3 years ago
  3. abtrehearn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[= e^{-3x}\int\limits\limits_{0}^{x}e^{3w} \sin w dw\]\[= (e^{-3x} + 3 \sin x - \cos x)/10.\]The solution, then, is\[y(x) = (e^{-3x} + 3 \sin x - \cos x)/10\]

    • 3 years ago
  4. abtrehearn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    for \[x \in [0, \pi), \]\[(e^{-3 \pi} + 1)/10, x \in [\pi, \infty).\]

    • 3 years ago
  5. Nisha318 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ewwww, my solution was wayyyy off.....we haven't learned convulution theorem yet....think we're covering that next. I'll post my solution in a minute....I tried working it out along with my professor's video.

    • 3 years ago
  6. Nisha318 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    My solution is 3 pages long....somebody please take a look at it and give me some feedback. See attached.

    • 3 years ago
  7. Nisha318 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Page 1

    • 3 years ago
    1 Attachment
  8. Nisha318 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Page 2

    • 3 years ago
  9. Nisha318 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    • 3 years ago
    1 Attachment
  10. Nisha318 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Page 3 (sorry, it was giving me trouble when trying to upload all 3 at one time.)

    • 3 years ago
    1 Attachment
  11. Nisha318 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    IN PDF

    • 3 years ago
    • Attachments:

See more questions >>>

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.