4325: Dynamical Systems - Homework 5

(C2.1) Solve for x by solving the decoupled 1st order ODE's.

$\begin{displaymath}\dot{x} = \left( \begin{array}{cc} 2 & 0 \\ 0 & -1 \end{array} \right)\cdot x \end{displaymath}$

(C2.2) Solve first for x₂(t) and then x₁(t).

$\begin{displaymath}\dot{x} = \left( \begin{array}{cc} -1 & 1 \\ 0 & -1 \end{array} \right)\cdot x \end{displaymath}$

(C2.3) Rewrite as a single first order ODE and solve for x₁(t)

$\begin{displaymath}\dot{x} = \left( \begin{array}{cc} 1 & 2 \\ -2 & 1 \end{array} \right)\cdot x \end{displaymath}$

From Strogatz: 2.3.4, 5.1.1, 5.1.2, 5.1.9(a,b).