# Coupled set of ODEs and Laplace Transform

1. Sep 18, 2012

### Niles

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
$$\frac{dX}{dt} = A + BY - CX$$
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:
$$L[X] = \frac{(C+Q+s) \left(-A B D F K+\left(-J (A B+s) (F+s)-A B \left(F H-\left(-G-\frac{L}{s}\right) (F+s)\right)\right) (R+s+\Sigma )\right)}{A B \left(-\frac{17}{18} A B D F R+(-A B F Q+(A B+s) (F+s) (C+Q+s)) (R+s+\Sigma )\right)}$$
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
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