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!

Help with Wronskian Equation

  1. Oct 9, 2014 #1
    1. The problem statement, all variables and given/known data
    W(t) = W(y1, y2) find the Wronskian.

    Equation for both y1 and y2: 81y'' + 90y' - 11y = 0

    y1(0) = 1
    y1'(0) = 0
    Calculated y1: (1/12)e^(-11/9 t) + (11/12)e^(1/9 t)

    y2(0) = 0
    y2'(0) = 1
    Calculated y2: (-3/4)e^(-11/9 t) + (3/4)e^(1/9 t)


    2. Relevant equations
    W(y1, y2) = |y1 y2 |
    | y1' y2' |
    3. The attempt at a solution
    After calculating y1 and y2, I don't seem to be able to do this determinant calculation. Mostly because it just doesn't look right, plugging in those giant equations and taking the derivative of them. Am I missing something here? Thanks for any help in advance.
     
    Last edited: Oct 9, 2014
  2. jcsd
  3. Oct 9, 2014 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Well, you didn't show us where these solutions came from so we can't check whether they are correct. But I suspect the idea isn't to calculate it directly like that. Does your text talk about Abel's theorem? There is a special equation that the Wronskian satisfies that relates ##W(0)## and the coefficients of your DE.
     
  4. Oct 9, 2014 #3
    Sorry, I have it now, and I have heard a little about Abel's Theorum, I'll try to find more information on it, thanks.

    Edit: I got it after abit of research on Abel's Theorum, thanks so much.
     
    Last edited: Oct 9, 2014
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Help with Wronskian Equation
  1. Wronskian help (Replies: 2)

Loading...