10.1 Theory of Linear Systems


Recall that in Section 3.12 we illustrated how to solve systems of n linear differential equations in n unknowns of the form


where the Pij were polynomials of various degrees in the differential operator D. In this chapter we confine our study to systems of first-order DEs that are special cases of systems that have the normal form


A system such as (2) of n first-order equations is called a first-order system.

Linear Systems

When each of the functions g1, g2, … , gn in (2) is linear in the ...

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