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Operational Determinants

  1. May 5, 2010 #1
    1. The problem statement, all variables and given/known data
    This is a problem in differential equations.

    Find the operational determinant and solve the equation.

    x'= 4x + y + 2t

    y' = -2x + y



    2. Relevant equations



    3. The attempt at a solution

    I'm at a total loss. All the examples in the book have problems with the form:

    (D - 4)x + 3y = 0
    -6x + (D + 7)y = 0

    Nothing like what I have, and certainly nothing with x,y, AND t. That t really throws me off.
     
  2. jcsd
  3. May 5, 2010 #2
    First when doing these problems put all the xs and ys on one side of the equations.
    So first you'll have
    x'-4x - y = 2t
    2x + y' - y = 0

    Now factor the differential operator "D" from the differentials. (I'm assuming x and y are functions of t)

    (D-4)x + 3y = 2t
    2x + (D-1)y = 0

    This gives you a way to find the operational determinant. To solve for a general solution you'll have to work a little more.
    Try the problem now..
     
    Last edited: May 5, 2010
  4. May 5, 2010 #3
    Thanks, it's much more clear now. I'll give the problem another try later.
     
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