Let x = x(t) be a twice-differentiable function and consider the second order differential equation x +
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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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a Making the change of variables y x ...View the full answer
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