1. Limited time only! Sign up for a free 30min personal 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!

A ode question

  1. Jul 10, 2010 #1
    1. The problem statement, all variables and given/known data

    y''+y'+y=0

    2. Relevant equations

    say we get the roots: -1/2+i*sqrt(3)/2 and -1/2-i*sqrt(3)/2

    3. The attempt at a solution
    I saw two solutions to this problem
    first is
    y=e^(-1/2*x)(c1*cos(sqrt(3)/2*x)+c2*sin(sqrt(3)/2*x))
    second is
    y=c1*e^[(-1/2+i*sqrt(3)/2)*x]+c2*e^[(-1/2-i*sqrt(3)/2)*x]

    which one is correct? I think the two solutions are different
    thanks
     
  2. jcsd
  3. Jul 10, 2010 #2
    Euler's Formula states:

    [tex] e^{i\theta} = \cos(\theta) + i\sin(\theta). [/tex]

    Can you fill in the remaining steps? I hope this helps.
     
  4. Jul 11, 2010 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Using Euler's formula, as Raskolnikov suggests, you should find that the two functions are the same. (Possibly different constants, of course.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A ode question
  1. ODE question (Replies: 2)

  2. ODE question (Replies: 1)

  3. ODE Question (Replies: 1)

  4. Question on ODEs (Replies: 0)

  5. ODE question (Replies: 9)

Loading...