Matrix exponential by the Laplace

Appendix B Matrix Exponential by the Laplace Transform Method... 

First order series/parallel chemical reactions and process control models are usually represented by a linear system of coupled ordinary differential equations (ODEs). Single first order equations can be integrated by classical methods (Rice and Do, 1995). However, solving more than two coupled ODEs by hand is difficult and often involves tedious algebra. In this chapter, we describe how one can arrive at the analytical solution for linear first order ODEs using Maple, the matrix exponential, and Laplace transformations. 

The matrix exponential can also be obtained by using the Laplace transform technique. Taking the Laplace transform of the governing equations now written in lower case X (see Ogata page 725).[1]... 

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