Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Undetermined coefficients to find general solution to system

  1. Sep 27, 2007 #1
    Hi,
    I'm having a bit of trouble with a problem here.

    The question is: Use the Method of undetermined coefficients to Find the general solution to th system:

    dx/dt = y + e^t
    dy/dt = -2x + 3y + 1

    I've got the homogenous solution fine, however I'm having a bit of difficulty with the particular solution.

    I used xp = [ ctwe^t + ue^t ] where w was [1,1]^T but i know this trial doesnt include the 1 term and is therefore incorrect.

    Can someone let me know what I'm supposed to do as a trial solution in this case. It's not explained in my notes, and I've looked online but to no avail.

    Thanks!
    Mike
     
  2. jcsd
  3. Sep 28, 2007 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What you give will work for the et part- though you really don't need the et- tet is enough. For the "1" you need to add a constant : say
    xp = [ (cte^t+ d)w ]
     
  4. Sep 29, 2007 #3
    hi,
    thanks for your help. I still cannot manage to get the solution. Is there anyway you can show some working I'd appreciate it?

    What I did:

    Let xp = [ (cte^t+ d)w ]

    therefore xp (differentiated) = cwe^t + cwte^t + 0

    Then Ax(t) + g(t)
    is cwte^t + [ b + 1 , -2a + 3b ]^T + [ e^t , 1 ]^T

    now we are supposed to equate to get the values of c, a and b but I cannot see how to do this...
    Thanks
     
  5. Sep 29, 2007 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What is A? You didn't mention that before. Is that the matrix mutliplying x in your original equation? If so you set that equal to the derivatives on the left. Because et is a solution to the homogenous equation, the terms involving tet will cancel out.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Undetermined coefficients to find general solution to system
Loading...