Chapter 4.6, Problem 69EQ

Let $x=x\left(t\right)$ be a twice-differentiable function and consider the second order differential equation

$x"+ax\text{'}+bx=0 \left(11\right)$

1. Show that the change of variables y = x' and

   z = x allows Equation (11) to be written as a system of two linear differential equations in y and z.

2. Show that the characteristic equation of the system in part (a) is ${\lambda }^2+a\lambda +b=0$.