Coupled set of ODEs and Laplace Transform

[Niles]

Homework Statement

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 won't 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.Niles.

 

[lippyka]

Homework EquationsThe equation for X is given as:\frac{dX}{dt} = A + BY - CXThe Laplace transform of X is given as: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)}The Attempt at a SolutionOne approach to finding the inverse of this equation is to use numerical methods, such as the finite difference method or the Runge-Kutta method. These methods can be used to approximate the solution of the differential equations and then find the inverse of the resulting numerical solution. These methods can be time consuming, but are often the only viable option when the solution of an equation cannot be found in any tables.