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!

Homework Help: First order system ODE, complex root

  1. Dec 3, 2012 #1

    For first order system ODE, complex root.
    y'=Ay, where A is a 2by2 matrix. I am assuming the roots are complex. After finding the eigenvalue (complex conjugate) and their eigen-vectors (which come in a form of complex conjugate again), we plug into the solution y=ζexp(λt), where λ is egenvalue and ζ is its corresponding eigenvector. And Since λ is complex, we apply euler's formula.And at the end, we get to the part
    y= u(t) + i*v(t).

    I don't understand why both u(t) and v(t) are solution to the system. u(t) is clear. But v(t) is not. what happen to its imaginary number?

    Last edited: Dec 3, 2012
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted