1. Not finding help here? Sign up for a free 30min 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!

Coupled set of ODEs and Laplace Transform

  1. Sep 18, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi

    I have a set of five coupled ODE, and I would like to find a solution to the first variable X in the set (the rest I call Y, Z, V, W). The equations are of the form
    [tex]
    \frac{dX}{dt} = A + BY - CX
    [/tex]
    This isn't homework, but something I been working with for some time. OK, so my strategy so far has been to first Laplace transform all five equations, and then solve for L[X], the Laplace transform of X. This I have done succesfully, however it yields a long expression. For convenience I list it here:
    [tex]
    L[X] = \frac{(C+Q+s) \left(-A B D F K+\left(-J (A B+s) (F+s)-A B \left(F H-\left(-G-\frac{L}{s}\right) (F+s)\right)\right) (R+s+\Sigma )\right)}{A B \left(-\frac{17}{18} A B D F R+(-A B F Q+(A B+s) (F+s) (C+Q+s)) (R+s+\Sigma )\right)}
    [/tex]
    In this equation all capital letters including Ʃ are constants (including initial conditions) and s is the variable. My original plan was to consult a table of Laplace transform in order to find the inverse, however I found out pretty quickly that it wont work as I can't find any of the terms in any table I have encountered.

    Do I have any other alternatives here? I would be happy to be pointed in the right direction.

    Best,
    Niles.
     
    Last edited: Sep 18, 2012
  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?



Similar Discussions: Coupled set of ODEs and Laplace Transform
  1. Laplace transform (Replies: 0)

  2. Laplace Transform (Replies: 0)

Loading...