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!

Solving Systems of Linear Differential Equations

  1. Jun 19, 2011 #1

    1. x' + y' - x = -2t
    x' + y' - 3x -y = t^2





    2. x' = Dx, y' = Dy





    3.
    I eliminated x to get y alone by multiplying the first row by (D-3) and the second row by (D-1)

    (D-1)(D-3)x + (D-3)Dy = -2t(D-3)
    (D-1)(D-3)x + (D-1)(D-1) = t^2(D-1)

    then subtracted to get: (D+1)y = -t^2 -4t + 2

    I put this into a differential equation form y' + y = -t^2 - 4t + 2 This is linear first order, and my integrating factor is e^t (at this point I will solve this linear ODE)

    For getting x by itself, I eliminated y by multiplying the first row by (D-1) and the second row by D

    (D-1)(D-1)x + D(D-1)y = -2t(D-1)
    D(D-3)x + D(D-1)y = Dt^2

    then subtracted to get: (D+1)y = -2

    I put this into a differential equation form y' + y = -2 This is linear first order, and my integrating factor is also e^t (at this point I will solve this linear ODE)



    I just need to know that I'm good up to here.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 19, 2011 #2
    First: your notation is a bit confusing. Also derivative operators (usually) act on the right, so you multiply them from the left, and therefore have -2 (D-3) t instead of -2 t (D-3). However, your result is correct, that is
    y' + y = -t^2 - 4t + 2. (the integrating factor e^t is also correct)

    Afterwards (in the second calculation) I think you confused y and x, since I get
    x' + x = -2.
     
  4. Jun 19, 2011 #3
    I recommend writing it in matrix notation.
     
  5. Jun 19, 2011 #4
    I have to use this method specifically for my homework assignment.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solving Systems of Linear Differential Equations
Loading...