1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

ODES with complex roots

  1. May 16, 2014 #1
    Hi, Im just having a little trouble with differential equations. I have y'' - 6y' + λy = 0
    I know I need complex roots and setting e^[itex]\alpha[/itex]x gives [itex]\alpha[/itex]= 3+/-sqrt(9 - λ). Then I don't understand why set -ω^2= 9-λ.

    How do you know if it is -ω^2 or w^2. Thanks for the help.
     
  2. jcsd
  3. May 16, 2014 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Complete the square on the characteristic equation:$$
    r^2 + 6r +\lambda = (r^2 + 6r + 9) +(\lambda - 9) = (r+3)^2 +(\lambda - 9) = 0$$So you have ##(r+3)^2 = (9-\lambda)##. For complex roots you need the right side to be negative so set$$
    9-\lambda=-\omega^2.$$This corresponds to ##\lambda > 9##.
     
  4. May 16, 2014 #3
    Thanks a lot. I appreciate it.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted