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!

Systems of first order linear equations involving wronskian and matrices

  1. Nov 27, 2011 #1
    1. The problem statement, all variables and given/known data

    If y3(0) = 2y2(0) - y1(0), what is W(3)?

    2. Relevant equations

    [itex]\frac{d}{dt}[/itex] y(t) = A(t) y(t),

    A(t) =
    [1 et e-t]
    [e-t 0 et]
    [2 sin(t) -1]

    3. The attempt at a solution

    I already solved the Wronskian W(t)=c*e∫(1+0-1)dt=c

    What I was not sure about was how to go about solving for the general solution of the y's.

    Would it be y3(t)=eAt*y3(0)?

    y3(t)=eAt*(2y2(0) - y1(0))
    where At =
    [t tet te-t]
    [te-t 0 tet]
    [2t tsin(t) -t]
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

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



Similar Discussions: Systems of first order linear equations involving wronskian and matrices
Loading...