Question: Let x = x(t) be a twice-differentiable function and consider the second order differential equation x + ax + bx = 0 (a) Show that

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

x′′ + ax′ + bx = 0

(a) 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.

(b) Show that the characteristic equation of the system in part (a) is λ² + aλ + b = 0.

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