Ordinary Differential Equations and Dynamical Systems Vol2 · Problem 2.2

Existence Theory

Mathematics — Calculus · matrix-exponential-second-order-ode

Problem

(a) Write the second order equation

u'' + 2u' + u = 0 \tag{2.5}

as a first order system

x' = Ax

. (b) Find

\exp At

for the matrix

A

in part (a). (c) Use the answer from part (b) to find the solution of (2.5) with

u(0) = u_0

and

u'(0) = u_1