A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Could someone tell me the steps of solving this 2nd order differential equation? (x^2)y'' - x y' + y = 8(x^3) Is it Euler's equations for the left side and method of undertermined coeffficients for the right side? Thanks!!!

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

    the A.E. is D^2 - D +1 =0 D= 1+- SQRT(3) i/ 2 yc= e^1/2 (C1 cos sqrt(3)/2 + C2 sin sqrt(3)/2)

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

    particular solution = 1/ (D^2 - D +1) * 8(x^3)

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

    sry an error in typing. yc= e^1/2 (C1 cos sqrt(3)/2 x + C2 sin sqrt(3)/2 x)

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

    ah again yc= e^1/2 x (C1 cos sqrt(3)/2 x + C2 sin sqrt(3)/2 x)

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

    why did you write: D^2 - D +1 =0 at the very beginning? Did you divide both sides by x squared?

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

    this is auxiliary equation

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

    yeah but you can't just ignore the x squared right? i know the quadratic formula but i am not sure if this is the case here

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

    still there buddy?

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

    ok give me a sec...

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

    so here we go...

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

    put z=logx and xD=theta , x^2D^2= theta (theta -1)

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

    1 sec

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

    Your way may work but I don't think I've seen it in class...it's gotta be easier than we think

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

    ok

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

    thanks a lot though

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

    you've been super helpful

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

    no prob... i wish i cud help u a lot more.. :(

  18. 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.