A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

UnkleRhaukus

  • one year ago

\[\frac{\mathrm dx}{\mathrm dt} = -4\pi^2x+x^2\] \[x_0 = \pi^2,\qquad v_0=0\]

  • This Question is Closed
  1. Empty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Is \(\pi\) the circle constant?

  2. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  3. Empty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I guess it appears to be a separable differential equation, unless there's some trick going on haha. This is kind of odd looking.

  4. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    numeric methods

  5. Empty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    It has a general solution \[x=\frac{4 \pi^2}{e^{4\pi^2 (c+t)}+1}\]

  6. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah, but how did you get that, I thought separable as well, but what is the numeric method :O

  7. Empty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I don't know, there are many numerical methods

  8. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the questing is asking me to use the leapfrog integration method, but i'm not convinced it is stable

  9. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @Astrophysics there was an x left over... usually when it's separable it would be in the form of h(y) dy = f(x) dx and then integrate both sides but that's not the case in this equation :/

  10. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ah ok, and I see leap frog method, is this a mechanics problem..mhm

  11. Empty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yeah, that's how I got my answer, partial fractions. This is separable @UsukiDoll

  12. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Wolfram confirms, I don't really know leapfrog integration very well, this does remind me of a simple harmonic oscillator, @Empty you know how to do it using the method

  13. Empty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Ok but the real question is, "How do I show that leapfrog integration is stable" and that I don't know.

  14. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    X( completely missed that... yes it is separable... (after hours...mind can't think). But what is leapfrog integration?

  15. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{\mathrm dx}{\mathrm dt} = -4\pi^2x+x^2 \] \[\frac{dx}{-4 \pi^2x+x^2} = dt\] \[\frac{dx}{x(-4 \pi^2+x)} = dt\] and then partial fractions... (not doing the rest)

  16. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Lol I don't think he's allowed to use that

  17. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    -_- k forget it *tosses it in the trash*

  18. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    was fun when it was legit.

  19. Astrophysics
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Haha have a medal, @Michele_Laino may be able to help you

  20. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Catastrophic, error sorrys

  21. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    nah... could be something I haven't done or idk... it's similar to asking me to do a PDE involving Laplace Equation at after 3 am. My brain can't function at this hour..

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.