We assume the reader is already familiar with first- and second-order linear ordinary differential equations (ODEs) with constant coefficients, either homogeneous or not. Here, we review results on the solutions to systems of N first-order linear ODEs.
We first consider the existence and uniqueness of a C1 solution X: [a, b] → to the problem
where is the given initial datum, Q is a given real N × N matrix and F : [a, b] → is a given continuous function.
Lemma C.1 (Grönwall) Let W C1(]a, b[, ) satisfy the inequality
for some α ≥ 0 and β > 0. Then
Proof. Let ∊ > 0. The function is strictly ...