A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

I have a question on complex roots. I have the eqn 8y'' +18y' +18y = 0, with the initial conditions of y(0)=3 and y'(0) = 4. I am trying to put this in the form y = Ae^rx +Be^rx, with my r = -9/8 +/- sqrt(126)....can anyone give pointers on getting the correct A and B? My answers are still wrong :(

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

    Hello!

  2. JamesJ
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Remember that \[ \sin bx = \frac{1}{2i} ( e^{bxi} - e^{-bxi}) \] and \[ \cos bx = \frac{1}{2} ( e^{bxi} + e^{-bxi}) \] So you can write your solutions as the product of a (real) exponential and of trig functions.

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

    In particular, if you find the roots to the characteristic equation are \[ \lambda = a \pm bi \], then the general solution to the homogenous 2nd order equation is \[ C_1 e^{ax} \cos bx + C_2 e^{ax} \sin bx \]

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

    Oh, okay. So when I know I will have complex numbers as a result of solving for my roots, how should I go about identifying where I should use this rule?

  5. JamesJ
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    whether you have roots which have a non-zero imaginary part

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

    Thanks so much!

  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.