A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

How to use undetermined coefficients for right hand side of this differential equation: y''+y'+8y = t*cos3t + (10t^2 +21t + 9) * sin3t

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

    This is a large problem to write out online, but you can tackle it by finding the particular solution as such. You can find particular solutions to each of\[y''+y'+8y=t \cos 3t\]and\[y''+y'+8y=(10t^2+21t+9) \sin 3t\]and add them to find the particular solution to the whole thing. To find the particular solution for the first equation set,\[y_1=(At+B)(C \cos 3 t + D \sin 3t)\]and for the second,\[y_2=(At^2+Bt+C)(D \cos 3t + E \sin 3t)\]Substitute each into your d.e. and find the coefficients. Your particular solution will then be\[y_p=y_1+y_1\]If you need any further help, let me know.

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

    you a fan of Nikola Tesla? and all his inventions?

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

    Thank you so much,lokisan. What I didn't get was, if I should write underdetermined coefficients for both polynomial and trigonometric function or just for trigonometric function -which are in multiplication- [ex. in my textbook (e^t * sint) is written in underdetermined coefficients as [e^t * (A*cost + B*sint)] Now I get i should write for both and look for if there are common coefficients (like if there are two A*D coefficient I could write A to simplify that,hope I got it right.

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

    You're welcome. Become a fan :D If you get stuck, let me know.

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

    oktal, you wasting time here and not studying?!

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

    oktal,yep,for sure!

  7. 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.